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IS"

THE DETERMINATION

HYDROGEN IONS

An elementary treatise on the hydrogen electrode, indi-
cator and supplementary methods with an indexed
bibliography on applications

W. MANSFIELD CLARK, M.A., Ph.D.

Formerly Chemist, Research Laboratories of the Dairy Division,

United Stales Department of Agriculture,

Professor of Chemistry, Hygienic Laboratory,

United States Public Health Service

SECOND EDITION

% l%o $

I O q 1<4.

BALTIMORE

WILLIAMS & WILKINS COMPANY

1923

QD
50, \

First Edition, September, 1920

Reprinted, May, 1921

Second Edition, September, 1922

Reprinted, May, 1928

Fellow Workers in the Biological Sciences,

Architects of Progress,

Who Hew the Stone to Build Where Unseen Spires Shall Stand

TABLE OF CONTENTS

I. Introduction. Some General Relations Among Acids

and Bases 15

The nature of electrolytic dissociation 15

Reversible reactions and chemical equilibria 16

The equilibrium equation for acid dissociation 18

The equilibrium equation for base dissociation 20

The water equilibrium 21

Titration curves 22

Percentage dissociation curves 24

Amphoters 30

II. Some Special Aspects of Acid-base Equilibria 34

" The pH scale 34

/ The effect of dilution 37

- Buffer action 39

The conduct of strong electrolytes 44

v/III. Outline of a Colorimetric Method 48

Color chart. Water color by Broedel, color press work

by F. Goeb between 50 and 51

IV. Theory of Indicators 54

Outline of the Ostwald theory 55

Tautomerism 59

Optical aspects 62

V. Choice of Indicators 73

Review of available material 74

S0rensen's selection 78

Clark and Lubs' selection 80

Michaelis' selection 82

Tables of indicators with their pH ranges 84-94

Indicator synonyms 95

VI. Standard Buffer Solutions for Colorimetric Comparison 99
Preparation of materials for Clark and Lubs' solutions. 100

Clark and Lubs' buffer solutions 106

Preparation of materials for S0rensen's solutions 107

S0rensen's solutions 111-114

Other solutions 115

VII. Sources of Error in Colorimetric Determinations 118

Salt errors 118

Protein errors 122

Other errors 123

Effect of temperature variation 123

VIII. Approximate Determinations with Indicators 126

Judgment by unaided eye 126

Gillespie's method 127

6 CONTENTS

Michaelis' method 132

Indicator paper 138

Dilution 139

Use of indicators in bacteriology 140

Special uses 142

Spotting ' 143

IX. Outline of the Electrometric Method 144

X. Theory of the Hydrogen Electrode 151

Potential differences between electrodes and solutions. . . . 151
Derivation of equation relating electrode potential dif-
ference to concentration 152

Equation for concentration chain 154

Derivation of numerical form of equation 155

The "normal hydrogen electrode." 157

Barometric correction 159

Final working equation 161

XI. Potential Differences at Liquid Junctions 163

The cause 163

Equations used in the calculation of liquid junction

potential differences 164

Experimental studies 167

The employment of saturated KC1 solutions 168

Summary of general conclusions 171

XII. Hydrogen Electrodes and Electrode Vessels 173

Construction of electrodes 173

Deposition of "black." 175

Hydrogen electrode vessels 178

XIII. Calomel Electrodes 191

The general principles and structure 191

Chemical preparation of calomel 191

Electro-chemical preparation of calomel 192

Variations of potential 192

Calomel electrode vessels 194

Values assigned to potential differences 195

XIV. The Potentiometer and Accessory Equipment 201

The principle of the potentiometer 201

A simple potentiometer 202

The Leeds and Northrup instrument 203

A resistance box system 205

Volt-meter, system 207

Ballistic galvanometer method of measurement 208

Use of the electron tube 210

Null point instruments 212

The galvanometer 212

The capillary electrometer 213

The quadrant electrometer 214

The telephone receiver 216

CONTENTS 7

Selection of null point instrument characteristics 216

Potentiometer characteristics 219

The Weston standard cell 221

Storage batteries 224

XV. Hydrogen Generators, Wiring, Shielding, Temperature

Control, Purification of Mercury 227

XVI. The Relation of Hydrogen Electrode Potentials to

Reduction Potentials 242

Relations based on assumption that reductant reacts with

hydrogen ion or with water 243

Difficulties encountered 245

The postulate of electron concentration 247

Electrode equation involving electron concentration 251

Coordination of electrode equations 251

Discussion based on the coordination 253

Some elementary relations of hydrogen ion concentrations

to observed "reduction potentials." 256

XVII. Sources of Error in Electrometric Measurements of pH. 264
XVIII. Standard Solutions for Checking Hydrogen Electrode

Measurements 271

XIX. The Standardization of pH Measurements 276

Absence of a precise basis 277 ~ *

Values used for standard electrodes 280 ct ft&tCfi

Necessity for standardization 286

Proposal of standard values 287

i Experimental definition of pH 287*5 Ml Uit *

XX. Supplementary Methods 289 cf fM f#

The quinhydrone electrode 289 \'^/icc0uOUf

Conductivity 293 fy /tfxsyfM

Catalytic decomposition of nitrosotriacetonamine 294 (/

Catalytic decomposition of diazoacetic ester 295

Inversion of cane sugar 296

Catalyses in general 296

Miscellaneous methods 296

XXI. Applications 298

General reviews 299

The theory of titration 299

General considerations 304

Subject index to bibliography 310

Bibliography 346

Appendix 456

Table A. Standard values for calomel electrodes 456

Table B. Showing the relation of [H+] to pH 456

Table C. Temperature factors for concentration chains 457

Table D. Correction of barometer reading for temperature 458

8 i CONTENTS

Table E. Barometric corrections for H-electrode potentials 459

ce a

Table F. Values of log and of log multiplied by the tem-

1 — oc 1— a

perature factors for concentration chains at 20°, 25°, 30° and

37?5C 460-461

Table G. Ionization constants 462-463

Logarithms of numbers 464-465

Index of authors mentioned in the text 467

Index of Subjects 471

PREFACE TO THE FIRST EDITION

Poincare" in The Foundations of Science remarks, "There are
facts common to several sciences, which seem the common source
of streams diverging in all directions and which are comparable
to that knoll of Saint Gothard whence spring waters which fer-
tilize four different valleys."

Such are the essential facts of electrolytic dissociation.

Among the numerous developments of the theory announced
by Arrhenius in 1887 none is of more general practical importance
than the resolution of "acidity" into two components — the
concentration of the hydrogen ions, and the quantity of acid
capable of furnishing this ionized hydrogen. For two -reasons the
hydrogen ion occupies a unique place in the estimation of stu-
dents of ionization. First, it is a dissociation product of the great
majority of compounds of biochemical importance. Second, it is
the ion for which methods of determination have been best
developed. Its importance and its mensurability have thus
conspired to make it a center of interest. The consequent group-
ing of phenomena about the activity of the hydrogen ion is
unfortunate when it confers undue weight upon a subordinate
aspect of a problem or when it tends to obscure possibilities of
broader generalization. Nevertheless, such grouping is often con-
venient, often of immediate value and frequently illuminating.
Especially in the field of biochemistry it has coordinated a vast
amount of material. It has placed us at a point of vantage from
which we must look with admiration upon the intuition of men
like Pasteur, who, without the aid of the precise conceptions
which guide us, handled "acidity" with so few mistakes.

In the charming descriptions of his experimental work Pasteur
has given us glimpses of his discernment of some of the effects of
"acidity" in biochemical processes. In the opening chapter of
Studies on Fermentation he noted that the relatively high acidity
of must favors a natural alcoholic fermentation in wine, while the
low acidity of wort induces difficulties in the brewing of beer.
He recognized the importance of acidity for the cultivation of
the bacteria which he discovered and was quick to see the lack of

10 PREFACE TO FIRST EDITION

such an appreciation in his opponents. In describing that process
which has come to bear his name Pasteur remarks, "It is easy
to show that these differences in temperature which are required
to secure organic liquids from ultimate change depend exclusively
upon the state of the liquids, their nature and above all upon the
conditions which affect their neutrality whether towards acids or
bases." The italics, which are ours, emphasize language which
indicates that Pasteur was aware of difficulties which were not
removed till recently. Had Pasteur, and doubtless others of like
discernment, relied exclusively upon volumetric determination of
acidity they would certainly have fallen into the pitfalls which
at a later date injured the faith of the bacteriologist in the meth-
ods of the chemist. Was it reliance upon litmus which aided
him? Perhaps the time factor involved in the use of litmus
paper, which is now held as a grave objection, enabled Pasteur
to judge between extremes of reaction which the range of litmus
as an indicator in equilibrium does not cover. At all events he
recognized distinctions which we now attribute to hydrogen ion
concentrations. Over half a century later we find some of
Pasteur's suggestions correlated with a marvelous development
in biochemistry. The strongest stimulus to this development
can doubtless be traced to the work of S0rensen at the Carlsberg
Laboratory in Copenhagen and not so much to his admirable
exposition of the effect of the hydrogen ion upon the activity of
enzymes as to his development of methods. At about the same
time Henderson of Harvard, by setting forth clearly the equilibria
among the acids and bases of the blood, indicated what could be
done in the realm of physiology and stimulated those researches
which have become one of the most beautiful chapters in this
science.

Today we find new indicators or improved hydrogen electrode
methods in the physiological laboratory, in the media room of
the bacteriologist, serving the analyst in niceties of separation
and the manufacturer in the control of processes. The material
which was admirably summarized by Michaelis in 1914, and to
which Michaelis himself had contributed very extensively, pre-
sents a picture whose significance he who runs may read. There
is a vast field of usefulness for methods of determining the hydro-
gen ion. There is real significance in the fruits so far won.

PREFACE TO FIRST EDITION 11

There remain many territories to explore and to cultivate. We
are only at the frontier.

In the meantime it will not be forgotten that our knowledge of
the hydrogen ion is an integral part of a conception which has
been under academic study for many years and that the time has
come when the limitations as well as certain defects are plainly
apparent. While there is now no tendency nor any good ground
to discredit the theory of electrolytic dissociation in its essential
aspects, there is dissatisfaction over some of the quantitative
relationships and a demand for broader conceptions. It requires
no divination to perceive that while we remain without a clear
conception of why an electrolyte should in the first instance
dissociate, we have not reached a generalization which can cover
all the points now in doubt. Perhaps the new developments in
physics will furnish the key. When and how the door will open
cannot be foreseen ; but it is well to be aware of the imminence of
new developments that we may keep our data as pure as is con-
venient and emphasize the experimental material of permanent
value. We may look forward to continued accumulation of
important data under the guidance of present conceptions, to
distinguished services which these conceptions can render to
various sciences and to the critical examination of the material
gathered under the present regime for the elements of permanent
value. These elements will be found in the data of direct experi-
mentation, in those incontrovertible measurements which, though
they be but approximations, have immediate pragmatic value
and promise to furnish the bone and sinew of future theory. In
the gathering of such data guiding hypotheses and coordinating
theories are necessary but experimental methods are vital.

The time seems to have come when little of importance is to
be accomplished by assembling under one title the details of
the manifold applications of hydrogen electrode and indicator
methods. It would be pleasing to have in English a work com-
parable in scope with Michaelis' Die W asserstoffionenkonzentra-
tion; but even in the short years since the publication of this
monograph the developments in special subjects have reached
such detail that they must be redispersed among the several sci-
ences, and made an integral part of these rather than an unco-
ordinated treatise by themselves. There remains the need, for a

12 PREFACE TO FIRST EDITION

detailed exposition, under one cover, of the two methods which
are in use daily by workers in several distinct branches of bio-
logical science. It is not because the author feels especially
qualified to make such an exposition that this book is written,
but rather because, after waiting in vain for such a book to
appear, he has responded sympathetically to appeals, knowing
full well from his own experience how widely scattered is the
information under daily requisition by scores of fellow workers.

For the benefit of those to whom the subject may be new
there is given in the last chapter a running summary of some of
the principal applications of the methods. This is written in
the form of an index to the bibliography, a bibliography which
is admittedly incomplete for several topics and unbalanced in
others, but which, it is believed, contains numerous nuclei for
the assembling of literature on various topics.

The author welcomes this opportunity to express his apprecia-
tion of the broad policy of research established in the Dairy Divi-
sion Laboratories of the Department of Agriculture under the
immediate administration of Mr. Rawl and Mr. Rogers. Their
kindness and encouragement have made possible studies which
extend beyond the range of the specialized problems to which
research might have been confined and it is hoped that the bread
upon the waters may return. To Dr. H. A. Lubs is due the credit
for studies on the synthesis of sulfonphthalein indicators which
made possible their immediate application in bacteriological
researches which have emanated from this laboratory. Acknowl-
edgment is hereby made of the free use of quotations taken
from the paper The Colorimetric Determination of Hydrogen Ion
Concentration and Its Applications in Bacteriology published in
the Journal of Bacteriology under the joint authorship of Clark
and Lubs.

The author thanks his wife, his mother, Dr. H. W. Fowle and
Dr. H. Connet for aid in the correction of manuscript and proof,
and Dr. Paul Klopsteg for valuable suggestions.

It is a pleasure to know that the publication of the photograph
of Professor S. P. L. S0rensen of the Carlsberg Laboratory in
Copenhagen will be welcomed by American biochemists all of
whom admire his work.

Chevy Chase, Maryland
March 17, 1920

PREFACE TO THE SECOND EDITION

The first edition of this book was offered to fellow workers for
the reasons stated in the preface. The rapid exhaustion of two
printings has revealed the extent of the demand for information
upon the topics discussed; but it has also brought to the author a
disquieting realization of the responsibility assumed at the first
venture, and regret that his preoccupation in a distinctive
although allied realm of research has prevented investigations which
might have contributed data for a more complete second edition.
This same preoccupation may be offered as an excuse for the
deficiencies in the bibliography and its classification. Over 900
new references have been added to the eleven hundred odd said
to be in the first edition; but, when it is realized that much of the
newer information is contained in papers neither the title nor
general subject of which would indicate that hydrogen ion con-
centrations have been considered, it will be appreciated that the
task of the bibliographer requires more time than an investigator
can afford. Indeed it will not be long before it will be as difficult
to trace this information as it has become to trace all the effects
of temperature. In certain fields of investigation "pH" is becom-
ing almost as common as "°C." Were it not that the introduction
of a new symbol would introduce confusion we would wish that
the special interpretation of pH given in Chapter XVII of the
first edition (Chapter XIX, this edition) could be symbolized by
°S (degrees S0rensen).

Certain chapters of the first edition have been rewritten and
all have been expanded to bring the book up to date and to meet
the very helpful suggestions given in the generous reviews of the
first edition, or by personal correspondence. It has been advis-
able, however, either to balance one suggestion against another
or to rely upon one's own judgment to maintain a balance in the
general treatment.

The question of a change of treatment to conform throughout
to the "activity" concept has been given serious consideration.
The author has been counseled by experienced teachers not to
attempt such a change, but his chief reason for definitely rejecting

14 PREFACE TO SECOND EDITION

the -proposal is simply that most of the data in use are still in
terms of the older conceptions. In the recasting of this data a
great deal of new experimental material must be collected and
the newer conceptions must be stabilized. Anything short of a
thorough revision of existing data would be but to cover the
subject with a thin veneer giving the appearance rather than
the substance of an up-to-date treatment.

The author is indebted to so many people for helpful sugges-
tions that it would appear ungracious to mention but a few. How-
ever, due credit must be given to Dr. Barnett Cohen for pains-
taking correction of proof, to Miss Florence Lansdale for clerical
assistance and to the publishers for their unfailing and courteous
cooperation.

Chevy Chase, Maryland
May 22, 1922

CHAPTER I

Introduction — Some General Relations Among Acids

and Bases

In a country rich in gold observant wayfarers may find nuggets on
their path, but only systematic mining can provide the currency
of nations. — F. Gowland Hopkins.

Why certain solvents such as water should cause or permit
the splitting of a compound into electrically charged bodies,
called ions, has not yet been very clearly explained. That they
do has been demonstrated with reasonable certainty. The evi-
dences are described in texts of physical chemistry and will not
be reviewed here, except as they are revealed in the verification
of the laws of chemical equilibria among electrolytes.

That aspect of electrolytic dissociation which is of special
interest to us may be conveniently pictured as follows.

A chemical element is conceived to be an aggregate of unit,
negative, electrical charges (electrons) grouped at relatively
enormous distances about a central, neutralizing nucleus of
positive electricity. The numerical value of this nucleus, in
terms of the number of electrons required for neutralization, and
the geometrical configuration of the positions of the surrounding
electrons are supposed to distinguish the several elements.

Certain of the electrons are but weakly incorporated in the
planet-like system of certain elements. When such an electron
has escaped, the element is left with a unit excess of positive
electricity. It is then a positive ion, a cation, having distinctive
properties.

If an element is so constituted that it can hold an extra electron,
the extra charge gives it new characteristics. The negatively
charged element is called an anion.

Certain compounds such as HC1 are made up of elements of
the two types mentioned above. On electrolytic dissociation HC1
oreaks up in such a way that the hydrogen atom loses an electron
ind this is taken up by the chlorine atom. HC1, thus, dissociates

16 THE DETERMINATION OF HYDROGEN IONS

into the positively charged hydrogen ion and the negatively
charged chlorine ion. The process may be represented as follows:

HC1?±H+ + Cl-
in the case of complex compounds such as acetic acid a similar
exchange of an electron occurs. The group CH3COO acts as a
unit and when negatively charged becomes the acetate anion.

Frequently an element or group can lose or acquire several elec-
trons. For instance Ca++ is the divalent cation of calcium and
SO4 is the divalent anion of the sulfate group — called divalent
because there are concerned two of those electrons which are sup-
posed to be intimately connected with the phenomenon of valency.

In passing it is interesting to note that the hydrogen ion is
unique. The element hydrogen is supposed to have but one
electron to the atom. When this is lost there is left the hydrogen
ion, a lone unit, positive charge.

Now this pictorial conception of the structure of elements,
while pregnant with possibilities, must not be considered vital
to the subject at hand. The one aspect which is vital is that
there occur dissociations whereby an element or group becomes
electrically charged — positively or negatively, as the case may be.
It is the electrical charge which turns an element or group into a
virtually new body and at the same time furnishes a handle, as
it were, with which we may lay hold on it by electrical devices.

On the other hand the electrical charge does not prevent a
limited application to ions of the laws of chemical equilibria.
Indeed it is among dilute solutions of certain electrolytically
dissociated compounds that there have been found the most
exact data supporting the laws of chemical equilibria.

It is with these laws of chemical equilibria that we are chiefly
concerned when dealing with the measurement of and the effects
of hydrogen ion concentration. Therefore, if electrolytic ioni-
zation be granted as a fact, it is only necessary to sketch the
concept of chemical equilibrium before coming to the simple, if
somewhat detailed account of the special manner in which the
concept is applied to acid-base equilibria.

Consider an acid of the type HA dissociating into tue cation
H+ (hydrogen ion) and the anion A-. The process may be
expressed as follows:

HA ^± H+ + A" (1)

GENERAL RELATIONS AMONG ACIDS AND BASES 17

Arrows are used to indicate that the process is reversible, —
that among the large number of anions and cations present in a
given volume some are recombining to form HA the while a
portion of the HA molecules are dissociating.

This concept of a "reaction" as labile, continuous, reversible
is of profound importance. So long as analysts are content to
balance the two sides of a written reaction with regard only to
the stoichiometrical relations, it is convenient to use the equation
sign and to forget the reality implied in the use of arrows. Reac-
tions do not go to completion and only approach completion
when by design or chance the proper conditions are supplied.
This reversibility of chemical reactions displays a world in flux.
From it the "everlasting hills" cannot escape; but upon it life bal-
ances its intricate organization. Often this is done so nicely that
the life of certain organisms is almost immortal.

In this interminable interplay of chemical reactions there occur
situations when on the statistical average a given reaction is pro-
ceeding no faster in one direction than in the other. In such
circumstances a chemical equilibrium is said to occur. Let us
formulate in as simple a way as possible the condition of a chemical
equilibrium.

Let brackets placed about a symbol indicate concentration of
the bracketed "species." Thus [HA] represents the concentration
of the residual, undissociated acid HA. Throughout the following
discussions we shall always let it be implied that by "concentra-
tion" is meant molar concentration. A molar solution is one
containing in one litre of solution that number of grams of the
indicated substance which is equal to its formula weight.

In equation (1) the rate at which the concentration [HA] is
being diminished because of the ionization may depend upon
several physical conditions. To know these is unnecessary for
the purpose at hand if we may assume that their effect on the
individual molecules of HA is constant on the statistical average.
Then, obviously, the rate at which reaction (1) proceeds from
left to right will depend upon the concentration of HA and some
constant factor which will be called ki.

Velocity left to right = ki [HA] (2)

The velocity of the reverse reaction wherein the ions recombine
to form HA might be supposed to be dependent only upon the

18 THE DETERMINATION OP HYDROGEN IONS

rate at which the ions in their thermal agitation collide. But it
is difficult to say what degree of approach is necessary for com-
bination or what other conditions must be fulfilled before the
combination can be considered to have taken place. It is much
safer then to assume only that some degree of meeting is necessary,
that some average state is to be considered virtual combination
and that the physical factors bringing about this state are, on
the statistical average, constant. Here again then we ascribe
the velocity of the reaction first to a factor dependent solely
upon the numbers of ions concerned [concentration] and second
another factor embracing all the known and unknown influences,
exclusive of concentration. Suppose then that we start with
equal numbers of H+ ions and A~ ions and double the concen-
tration of H+. Evidently the number of collisions of H+ ions
with A- ions will double. Likewise, if [A-] is doubled, the number
of collisions of A- with H+ ions will be doubled. If both are
doubled, the collisions are quadrupled. Consequently the velocity
of association, in so far as it is dependent upon the concentrations
of the reactants, is proportional to the product of these concen-
trations. Introducing the unknown proportionality factor repre-
senting the constant effect of all physical influences, we have :

Velocity right to left = k2 [H+] [A-]. (3)

We have already said that the state of equilibrium occurs when
the velocity of the reaction in one direction equals the velocity in
the reverse direction. Then at once by combining (2) and (3)
we have:

[H+] [Aj _ kx ,

[HA] ~ k2 ~ Ka W

For the ratio of two constants there is substituted in (4) another
constant, Ka, known as the equilibrium constant. This equilib-
rium constant when applied to electrolytes is known as the
ionization or dissociation constant.1

1 It should be particularly noted that in equation (4) the brackets
symbolize the concentrations occurring at the equilibrium state. When-
ever numerical values are to be introduced it is to be assumed that there
will be employed the same unit of concentration that was used in the experi-
mental derivation of Ka, and also the conventional form of the ratio with
the ions in the numerator.

GENERAL RELATIONS AMONG ACIDS AND BASES 19

Since equation (4) deals with the active masses of the reactants
it is a special application of the so-called law of mass action which
states that the velocity of a reaction is proportional to the product
of the concentrations of the reactants.

Using equation (4) for a particular acid it will be seen by inspec-
tion of the equation that if [H+] is increased, as by the addition
of another acid, there must be a readjustment of either [A-] or
[HA] or both to keep Ka constant. Likewise if [A~] should be
increased by the addition of a highly dissociating salt of the acid in
question, there would be a readjustment of either [H+] or [HA] or
both to keep Ka constant. Thus the independent alteration of
the concentration of any one of the species included in the equi-
librium equation causes a displacement of the equilibrium to a
new position. This illustrates how difficult it is to keep track of
the affair unless use is made of the simple algebraic relations.

If the acid alone be present, [H+] = [A-]. Substituting [H+]
for [A-] and solving equation (4) for [H+] we have

[H+] = VKa [HA]

If the acid is so weak that practically all is in the undissociated
form, no great error is made in putting [HA] equal to the con-
centration [S] of the total acid. Then [H+] = VKJS]".

In general it can be shown that for any reaction such as

A + B + C + . . . . . ;=± A' + B' + C +

the equilibrium condition is:

[A] [B] [C] . . .

[A'] IB'] [CI

= k

From the assumptions introduced in the argument it is evident
that the equilibrium constant will hold good only so long as there
are maintained constant those physical conditions which affect
the velocity of a reaction in one direction or the reverse. A
change in temperature will alter the "constant," but not to such
an extent as will a change in solvent. With due regard for such
matters we may regard the equilibrium constant as a number
characteristic of a given reaction at the equilibrium state.

In the derivation of the equilibrium equation we have employed
as an example the electrolytic dissociation of an acid. We may

THE DETERMINATION OF HYDROGEN IONS

now state that all substances capable of yielding hydrogen ions
must be considered as having an acidic nature and their conduct
in solution must be governed by the equilibrium equation.

With the ionization constant denned we are prepared to give
quantitative significance to comparative "strengths" among acids.
Inspection of equation (4) shows at once that if Ka is large the
numerator of the left hand side must be large in relation to the
denominator. In other words an acid having a relatively high
Ka value will, if left to itself in solution, tend toward a high degree
of dissociation. A given over-all concentration of an acid with
high dissociation constant will furnish a higher concentration of
hydrogen ions than will the same over-all concentration of an
acid with low dissociation constant. Thus the value of Ka at
once indicates the "strength" of an acid so far as "strength" is
measurable in terms of ionization.

In the following table are given a few dissociation constants
of acids and also of bases.

TABLE 1

Showing acidic and basic dissociation constants and their relation to a rough

classification of acids and bases

CLASS

COMPOUND

DISSOCIATION CONSTANT

Strong acid

Hydrochloric
Oxalic (first H)
Acetic
Boric

Sodium hydroxid
Ammonium hydroxid
Aniline

Not well defined

Weak acid

1.1 X 10"1
1.8 X 10_s

Very weak acid

6.5 X 10_1°

Strong base

Not well defined

Weak base

1.8 X 10-s

Very weak base

4.6 X 10~10

The dissociation of bases will now be considered. Just as a
substance ionizing to give hydrogen ions is called an acid so a
substance which ionizes to give hydroxyl ions (OH-) is called
a base.

The reversible reaction NaOH ^ Na+ + OH~ may be written
as BOH ^± B+ + OH- where B represents any monovalent
metal. This reaction may be treated in precisely the same way
that reaction (1) was treated. The equilibrium condition is: —

[B+] [QH-
[BOH]

= Kb

(5)

GENERAL RELATIONS AMONG ACIDS AND BASES 21

Just as the value of Ka is characteristic of a given acid so is
the value of Kb characteristic of a given base.

A very important relationship between acids and bases in
aqueous solution is brought about by the conduct of water.
It dissociates into the hydrogen ion (H+) characteristic of acids
and the ion characteristic of bases, OH-, called the hydroxyl ion.
The equilibrium of the reversible reaction HOH ^± H+ + OH- is
represented by

[H+] [OH-] _
[HOH]

Because the concentration of the undissociated water is so
large in relation to the dissociation products, [HOH] will not be
changed appreciably by the slight dissociation. [HOH] may
therefore be considered a constant and combined with k. Then
the above equation becomes:

[H+] [OH-] - Kw. (6)

It follows from this equation that, no matter how concentrated
the hydroxyl ions may be, there must remain sufficient hydrogen
ions to satisfy the above relation.2 This permits us to speak of
the hydrogen ion concentration of alkaline solutions and, as will
be shown presently, to construct a scale of acidity-alkalinity in
which we do not discriminate between hydrogen and hydroxyl
ion concentration.

Starting from equations (4), (5) and (6), applying certain
approximations and then using graphic methods of presentation
we can present a generalized picture of the conduct of acids and
bases similar to that first used by Henderson (1908). The final
simplicity of the picture warrants what may at first appear to be
a complicated reconstruction of the above equations.

In order to emphasize the hydrogen ion concentration as the
quantity in equation (4) with which the other species keep in
adjustment, let us rewrite equation (4) as follows:

1 [A-]

[H+] Ka[HA]

* Kw = 10-14. If in an alkaline solution the concentration of hydroxyl

*. Kw in-14

ions is 0.01 normal (10~2), [H+] = : — ^-r = =— = 10"12 N.

[OH"] 10~2

THE DETERMINATION OF HYDROGEN IONS

We choose the form which will give the reciprocal of [H+]
because we shall have to make use of the logarithm of this value
under the symbol pH for reasons which will appear later. For
the present let it be granted that it will be found convenient to

use log rather than [H+]. Taking the logarithm of each

[H+J

side of the above equation we have

i i . i, . [Ai

log • = log 1- log ;

[H+] Ka * [HA]

(7)

I A

■

(

> i

* 10

Fig. 1. Comparison of Experimental' Titration Curve of Acetic Acid
with Theoretical Approximation

With the use of this equation we can chart some important
relationships. Let it first be applied to what may be called
"titration curves."

Suppose we titrate 10 cc. of 0.2n acetic acid with 0.2n sodium
hydroxid. Ordinarily no attention would be given to the state
of the solution until the so called "end point" of the titration
were reached. In the present instance we shall follow the course
of the titration from the beginning by determining after each
addition of alkali the hydrogen ion concentration.

GENERAL RELATIONS AMONG ACIDS AND BASES

The experimental curve is plotted in figure 1. Let us com-
pare it with the values obtained by the use of equation (7) .

In the first place acetic acid is classed among the moderately
weak acids. Its dissociation constant as given in Landolt-

Bornstein is 1.82 X 10"5 at 18°C. Hence log =r = 4.74. Be-

-t»-a

TABLE 2

Comparison of log 1/[H+] for acetic acid-sodium acetate calculated by means of

the approximation formulated in equation (8) and determined

experimentally by Walpole

N/5 NaOH

RATIO

[salt]
[acid]

LOG RATIO

log 1/Ka

LOG 1/[H+]
CALCULATED

LOG 1/[H+]
WALPOLE

cc.

0.20

9.00

-1.69

4.74

3.05

3.08

0.25

0.020

-1.59

4.74

3.15

0.30

0.026

-1.51

4.74

3.23

3.20

0.40 .

0.031

-1.38

4.74

3.36

3.32

0.50

0.042

-1.28

4.74

3.46

3.42

0.75

0.053

-1.09

4.74

3.65

3.59 .

1.0

0.081

-0.95

4.74

3.79

3.72

2.0

0.111

-0.60 m

4.74

4.14

4.05

3.0

0.250

-0.37

4.74

4.37

4.27

4.0

0.429

-0.18

4.74

4.56

4.45

5.0

0.667

0.00

4.74

4.63

6.0

1.000

+0.18

4.74

4.92

4.80

7.0

1.500

+0.37

4.74

5.11

4.99

7.5

2.33

+0.48

4.74

5.22

5.09

8.0

3.00

+0.60

4.74

5.34

5.23

8.5

4.00

+0.75

4.74

5.49

5.37

9.0

5.67

+0.95

4.74

5.69

5.57

9.5

19.00

+1.28

4.74

6.02

5.89

9.625

25.67

+1.41

4.74

6.15

6.02

9.75

39.00

+1.59

4.74

6.33

6.21

9.875

79.00

+1.90

4.74

6.64

6.52

cause of the small dissociation of acetic acid (less than 2 per cent
in 0.2n solution even with no acetate present) the concentration
of the undissociated residue [HAc] is approximately equal to the
concentration of the total acetic acid. It is characteristic of the
alkali salts of acids that they are very highly dissociated. There-
fore, when sodium hydroxid is added to the acetic acid solution,
the resulting sodium acetate furnishes the greater amount of the

24 THE DETERMINATION OF HYDROGEN IONS

total acetate (Ac~) ions. As an approximation therefore we

[A-] [salt]

may substitute for the ratio 7777", in equation (7) the ratio 7 — — •

[HA] [acid]

Equation (7) then becomes:

log J_ =log-L + log^-j. (8)

*[H+J &Ka *[acid]

[ salt]
In table 2 are given the ratios r — 77. calculated from the num-

[acid]

ber of cubic centimeters of 0.2n alkali added to 10 cc. of 0.2n

acetic acid. Then follow the logarithms of these ratios, the value

of log z?~ for acetic acid, and log 7777; calculated from these data

-TV a L-H- J

by means of equation (8). Finally in the last column are given

the values of log ,777; calculated by Walpole (1914) from his

l**TJ
hydrogen electrode measurements. The experimental values

pH = log 7777; are plotted in figure 1 as circles while the values
LJfcr«-j

calculated by means of the approximation equation (8) are on the

unmarked line. There is evidently a substantial agreement with

a more or less regular discrepancy which remains to be explained.

The discrepancy may be ascribed in part to the assumption that

the salt is wholly dissociated and that it is entirely responsible

for the anions of equation (7). If there be applied a correction

for the partial dissociation of the acetate, there is obtained a

much closer agreement.

But even this correction does not take into consideration cer-
tain minor points, and it leaves untouched both the accuracy with
which Ka has been determined and the comparability of data
obtained by widely different methods which are often applied
(sometimes uncritically) in making such calculations as those
indicated above.

We shall proceed with the approximate treatment to bring out
certain more general relations, and shall leave to Chapter XXI
their further application to ordinary titrations.

[salt] 1

In equation (8) when the ratio f — rrr equals one, log J777; =

log 77 Then [H+] = K..

GENERAL RELATIONS AMONG ACIDS AND BASES 25

In other words the middle portion of the titration curve of a
particular acid lies at ("near" if we are# to be strict) a point
where the hydrogen ion concentration is numerically equal to the
dissociation constant.3

Thus if one wishes a solution of [H+] = 1 X 10~5, an acid with
dissociation constant close to this value is selected and mixed
with the proper amount of its alkali salt.

Or to look at the matter from another point of view, if we
determine the half transformation point in the titration of a
weak acid, we know approximately the dissociation constant of
the acid.

A similar set of relationships can be constructed for bases.

Instead of putting the fundamental equation (4) into the
form which we have utilized in following titration curves it is
sometimes advantageous to use the following development.

Transforming (4) we have :

[A-] _ Ka
[HA] [H+]

Now let us represent the concentration of the total acid by [S].
Then the concentration of [HA] will be :

[HA] = [S] - [A-]

[A~] Ka

[S]-[Ai [H+]
or

[A-] Ka

[S] Ka + [H+]

[A-]
The ratio -rrr- is the ratio of the dissociated acid to the total acid
L»J

present in the solution. This ratio may be represented by a.
Hence,

Ka + [H+]

(9)

3 There is implied in this the maintenance of the customary unit of
concentration. Cf. page 18.

26 THE DETERMINATION OF HYDROGEN IONS

/ 1 \ /^ — \

Since we are interested in log rrrp: or pH rather than [H+], because

of the resultant simplification of chart representations and because
of other reasons which will appear later, we may recast equation
(9) and taking the logarithm of each side we have :

11 ot

log = log h log — (10)

* [H+] * K. * (1 - «)

Plotting log } which is pH, against «, and expressing « as

[H+J

percentage dissociation, there is obtained a curve such as A or B
in figure 2. Such curves are identical in form, the form being

Ot *

determined by the ratio — • Their position on the pH axis

(1 - «)
is determined by the value of the dissociation constant in the

expression log —

Since (10) is useful in plotting type curves a table of values for

log is given in the appendix (p. 460).

1 — a

(11)

In a similar way we arrive at the relation for bases :

a= Kb

" Kb + [OH-]
or

logfOHi^log1^1"00- (12)

But since we wish to deal uniformly with log jTT^f, which is pH,

rather than with the hydroxyl ion concentration or any direct
function thereof, we shall introduce the water equilibrium, equa-
tion (6). Then (12) becomes

logJEz. = log?EiiL^

[H+] «

pH = log-L = log |^ + log 9—-^ (13)

[H+] Kw ot

GENERAL RELATIONS AMONG ACIDS AND BASES

With the introduction of Kw, the dissociation constant of water,
into our equations it becomes advisable to consider its numerical
value. Kw has been determined in a variety of ways of which
the following are examples. Kohlrausch and Heydweiller (1894)
determined the electrical conductivity of extremely pure water.
Assuming that the conductance is proportional to the mobility of

Fig. 2. Dissociation Cueves and Dissociation-Residue Curves

A. Dissociation curve of acid, log — = 8.0.

B. Dissociation curve of acid, log — = 4.8.

C. Dissociation-residue curve of acid, log — = 4.8, or dissociation curve

of a base log — = log — - — 4.8.
Kb Kw

the hydrogen and the hydroxyl ions, and that these are present in
equal concentrations, their product is found to be 1.1 X 10~14.
The hydrolysis of methyl acetate having been found to be pro-
portional to the concentration of hydroxyl ions, Wijs (1893)
determined the hydrolysis by water and found Kw = 1.44

X io-14.

By determining the hydrogen ion concentration with the
hydrogen electrode in solutions of known hydroxyl ion con-
centration (as determined by conductance measurements), Kw
is obtained from the product of the concentrations of the two ions.

THE DETERMINATION OF HYDROGEN IONS

By this method Lewis, Brighton and Sebastian (1917) found
the value 1.012 X 10"14 at 25°C.

Kolthoff (1921) has compiled the following table showing the
dissociation constant of water at different temperatures as given
by different authors and methods:

TEMPER-
ATURE

0°

0.12 X 10"14

0.14 X 10~"

0.089 X 10-"

18°

0.59 X 10~14

0.72 X 10""

0.74 X 10~"

0.46 X 10""

25°

1.04 X 10""

1.22 X 10""

1.27 X 10""

0.82 X 10-"

50°

5.66 X 10~"

8.7 X 10""

100°

58.2 X 10~14

74.0 X 10~14

48.0 X 10-"

I. Kohlrausch and Heydweiller recalculated by Heydweiller (1909).

II. Lorenz and Bohi (1909).

III. Michaelis (1914).

IV. Noyes and coworkers (1907).

The following values of log zz~ given by Michaelis (1914) were

X\-W

obtained on a somewhat different basis from that used by Lewis,
Brighton and Sebastian (1917).

Since in pure water [H+] = [OH"], [H+] or [OH~] = VKW.
Hence from the datum of Lewis, Brighton and Sebastian the
normality of H+ or OH- in pure water at 25°C. is VKW = 1.006
X 10~7 (practically pH = 7.0).

In the following pages wherever we have occasion for purposes
of illustration to use a numerical value for Kw we shall employ the
rounded value 10-14.

Introducing the numerical value of Kw into equation (13)
we have the convenient form :

1 , (1 — «)
pH = 14 - log -=- + log i 1

Kb a

(14)

In figure 2 we have plotted a as percentage dissociation. It is
obvious that the percentage dissociation residue will give the
complement of the dissociation curve and will cross any partic-
ular one of these at the fifty per cent dissociation point. See, for
example, the curve C of figure 2.

GENERAL RELATIONS AMONG ACIDS AND BASES

Now by comparing equation (10) with equation (14) it is found
that the curve for the dissociation-residue of an acid is identical
with the curve for the dissociation of a base when Ka of the acid

is related to Kb of the base as log ^r = 14 — log — . In other

TABLE 3

TEMPERATURE

LOGTf—
KW

pH OP NEUTRAL POINT

14.200

7.10

14.165

7.08

14.130

7.07

14.100

7.05

14.065

7.03

14.030

7.02

13.995

7.00

13.960

6.98

13.925

6.96

13.895

6.95

13.860

6.93

13.825

6.91

13.790

6.90

13.755

6.88

13.725

6.86

13.690

6.85

13.660

6.83

13.630

6.82

13.600

6.80

13.567

6.78

13.535

•6.77

13.505

6.75

13.475

6.74

13.445

6.72

13.420

6.71

words curve C (fig. 2) is either the dissociation-residue curve of
an acid for which log — = 4.8 or the dissociation curve of a base

for which log— = 9.2 (since 14 - 9.2 = 4.8).

lVb

The importance of this relation lies in the fact that a deter-
mination of the effect of hydrogen ion concentration on some
process may not reveal whether the phenomenon has to do with

30 THE DETERMINATION OF HYDROGEN IONS

an acid or a base, unless an independent method reveals the nature
of the active substance.

The student will find it interesting to plot dissociation curves for acids
with percentage dissociation as one coordinate and pH as the other, and

then dissociation curves for bases with log .„„_. (which may be called

pOH) as one of the coordinates plotted inversely as pH. At a given temper-
ature and given value for Kw there is a fixed value for pOH at each value
for pH. This follows directly from equation (6) ; and it is particularly to
be noted that in deriving this relation we need not fix the position of the
pOH scale in its relation to the pH scale by confining our attention to the
special case where [H+] = [OH-], occurring roughly at pH 7.0. Indeed the
so-called neutral point (pH 7.0) may be considered only as a convenient,
mental reference point having comparatively little physical significance.
It is not the point to which titrations are led, except under the rare con-
dition that the acid and the base are of exactly equal strength; and it is
of far less importance for amphoteric electrolytes than is the isoelectric
point of the given ampholyte.

Having plotted the two systems mentioned above the student will find
it interesting to assume that for moderate variations of temperature the
dissociation constants of acids and bases do not change seriously, and then
to note the shift in the two systems relative to one another when Kw is
altered with temperature.

The treatment accorded simple acids and bases may be ex-
tended to poly-acidic acids and poly-basic bases as well as to
those compounds containing both acidic and basic groups which
are called amphoteric electrolytes. It seems to be true very often
for such compounds that they dissociate in steps as is illustrated
in the titration curve of the tri-acidic phosphoric acid shown on
page 41. In this, as in many other cases, the several dissocia-
tion constants are of such widely different magnitudes that, when
we plot the dissociation curves as if of separate acids possessing
these dissociation constants, the curves do not seriously overlap.

Such acids may therefore be treated as if composed of two or
more independent acids. The effect produced when two dissocia-
tion constants lie closer together is illustrated by the titration curve
of o-phthalic acid shown on page 273. If in this case the formal
dissociation curve of a simple acid be plotted over the main
position of each section of the phthalate curve, it will be found
(as shown by Acree) that the experimental curve follows very
closely the interpolated resultant of the two formal single curves.

GENERAL RELATIONS AMONG ACIDS AND BASES

For amphoteric electrolytes (i.e., electrolytes containing acidic
and basic groups) a relation of great importance to protein chem-
istry may be illustrated by -the conduct of the simple ampholyte,
p-amino benzoic acid. The acid dissociation constant Ka is
6.8 X 10~6 and the basic dissociation constant Kbis 2.3 X 10-12
(Scudder). Translating these into the corresponding pH values
we have 5.17 and 2.36. If we regard the compound as if it were
made up of an acid and a base with the above dissociation con-

Fig. 3. Dissociation and Dissociation-Residue Curves op p-Amino-

benzoic Acid
Treated as if the amphoteric electrolyte were composed of an acid of

log — = 5.17 and a base of log — = log — — — 2.36.
Ka Kb Kw

stants (in terms of pH) and each independent of the other, we
can plot the dissociation curves of each with the aid of equations
(10 and 14). In each case the dissociation-residue curves are the
complements. These are plotted in figure 3 with heavy lines.
It is seen that they cross at pH = 3.77. This means that at
pH = 3.77 there is a maximum of undissociated residue. Now
if the salts are more soluble than the free compound itself there
should be a minimum solubility at pH 3.77. Michaelis and David-
sohn (1910) found a minimum solubility at pH 3.80.

Turning again to the light lines A and B of figure 3, we see that
their intersection is at a point where the percentage of the com-

32 THE DETERMINATION OF HYDROGEN IONS

pound ionized as an anion is equal to the percentage ionized as
a cation. In other words the amount carrying a negative charge
is equal to the amount carrying a positive charge. Because of
this equality the point where it occurs is called the isoelectric
point.

If we still maintain the simple conditions postulated in this
elementary treatment, we can calculate the isoelectric point from
the dissociation constants of an amphoteric electrolyte.

Consider an amphoteric electrolyte of the type HROH for
which we have the following equilibrium equations:

[HR+] [OH-

[HROH]
[ROB] [H+]

= Kb (15)

- Ka (16)

[HROH]

When [HR+] = [ROH] (isoelectric condition)

[HROH] _ [HROH]
b [OH-] " a [H+]

Hence [H+] - W— K (17)

"Kb

In the case cited above [H+] = W '^ — •— ; 10-14

2.3 X10-12

or pH = log ^— = 3.77

P * [H+

Furthermore from equations (15) and (16)

[HR+] + [ROH-] - Kb [HROHHH3 + [HROH]

Kw lH+]

If we let [HR+] + [ROH-] = X, X becomes a minimum when

0, a condition fulfilled when [H+] = J^ K,

d [H+] ' L J IK

In other words the sum of the anion and cation concentrations
is a minimum at the isoelectric point.

Only in case Ka = Kb will the isoelectric point correspond with
the "neutral point."

GENERAL RELATIONS AMONG ACIDS AND BASES 33

It is at once evident that the isoelectric point of an amphoteric
electrolyte is a point at or near which there should tend to occur
maximal or minimal properties of its solution. Indeed at such
points have been found to occur minimum solubilities, minimum
viscosities, minimum swelling, optimum agglutinations, etc.

It should be emphasized that the foregoing relationships have
been developed from very simple conditions. When these con-
ditions have been approached experimental verification has been
found. The insight thus gained has led to a better understanding
of complex ampholytes, the complete equilibria of which can
be seen only in broad outline. In attempting to formulate
more precisely the equilibrium equations which hold under more
complex conditions than those postulated above, Michaelis (1920)
has started with the influence of uni-univalent salts upon a simple
ampholyte and has then extended his propositions to cover the
influence of divalent ions and the influence of micelle formation.
It is of special interest to note that he can account for the dis-
placement of the precipitation optimum from the isoelectric
point by the influence of salts and that he finds it necessary to
caution against considering the isoelectric point to be always
identical with the point of maximum dissociation residue. He
also outlines the direction in which various relations will be
modified by the aggregation of the undissociated ampholyte
into micelles.

SUPPLEMENTARY REFERENCES

Texts on the principles of electrolytic dissociation : LeBlanc, Jones, Nernst,

Ostwald, Stieglitz (1917).
Generalized relations among acids and bases: Henderson (1908), Michaelis

(1914, 1922), S0rensen (1912).

CHAPTER II

Some Special Aspects of Acid-Base Equilibria

Words are the footsteps of reason. — Francis Bacon.

In the foregoing chapter we have outlined the chief aspects of
acid-base equilibria. We now have to discuss in more detail
some of the terminology of special use in acid-base studies and
also certain important matters which are continually met in
dealing with that class of electrolytes called the "strongly dis-
sociating" acids, bases and salts.

THE pH SCALE

v When "acidity" was resolved into its two components the nor-
mality unit was retained for each. As a normal solution of an
acid had been defined as one containing in 1 litre of solution the
equivalent of 1 gram atom of acidic hydrogen, so the normal solu-
tion of the hydrogen ion was defined to be one containing in 1
litre of solution 1 gram atom of hydrogen ions.1

To distinguish between these two components with their com-
mon unit it has been suggested that we call "normality" in its
older sense the quantity factor of "acidity" and the hydrogen ion
concentration the intensity factor. This may serve to emphasize
a distinction, but the suggested analogy with the quantity and
intensity factors of energy is confusing when we retain for each
a unit of the same category. Nevertheless the two components
remain in a restricted sense the quantity and intensity factors of
"acidity." The one is the total quantity of available acid. The
second, the concentration of the hydrogen ions, represents the
real intensity of "acidity" whenever it is the hydrogen ion which
is the more directly active participant in a reaction. This is
admirably expressed when we use for hydrogen ion concentrations
a mode of expression which links it with the potential of a hydro-
gen electrode. It so happens that in determining the hydrogen

1 It makes little difference whether the atomic weight of hydrogen be
taken as 1.008 or as 1.0 in calculating [H+].

34-

SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 35

ion concentration with the hydrogen electrode the potentials of
this electrode are put into an equation which reduces to the
form :

Potential , 1

= log

log frr+i tne symbol PH+

Numerical factor [H+l

Thus log r7jqT is at once obtained by the most simple of calcula-
tions. S0rensen (1909) saw that this value serves to define a
hydrogen ion concentration quite as well as [H+] itself and in his
Enzyme Studies' II, he used this mode of expression and gave to

[H-

As a matter of typographical convenience2 we shall adopt pH
in place of PH+. Since this is coming into wide usage its uniform
adoption is recommended in place of the bothersome variations3
which have made their way into the literature.

Although S0rensen has not revealed the considerations which
led to the choice of the letter P in his symbol, we might regard P
as suggesting the potential (intensity) factor of acidity in the
sense described above.

Writing the potential equation given on page 154 as

W = EF = RTln =tj
*At*. [H+]

it will be seen thatuE is the intensity factor in the work required
to carry a gram atom of hydrogen ions from concentration [H+]
to concentration 1 normal; and pH is a linear function of E.

pH is sometimes called the S0rensen value or S0rensen unit
and following S0rensen's original suggestion it is named the
hydrogen ion exponent. The last mentioned name must be used
with some caution because of a difference in sign between a
given pH value and the exponent occuring when the normality
of the corresponding hydrogen ion concentration is written. For

2 As is the custom of the Journal of Biological Chemistry.
J 3 Certain punctilious authors have insisted that the original symbol
should be retained but have made the mistake of assuming it to be PH-
The following variations are found in the literature:

ph,pH,Ph,PH,Ph,PH,Ph,PH, also each case italicised.

36 THE DETERMINATION OF HYDROGEN IONS

examples — 7 is the exponent in 10-7, but the pH value correspond-
ing to [H+] = 10-7n is +7.

The convenience of pH over [H+] is manifest when we compare
the numerical values encountered in chemical and physiological
studies. For instance, one enzyme may operate most actively at
a hydrogen ion concentration of 0.01 normal while another is
most active at 0.000,000,001 normal. While convenient abbre-
viations of such unwieldy values are 1 X 10~3 and 1 X 10~9,
there remains the difficulty of plotting such values on ordinary
cross-section paper. If the difference between 0.000,000,001 and
0.000,000,002 is given a length of one millimeter, the difference
0.01 to 0.02 when plotted on the same scale would be ten kilo-
meters, ten kilometers distant. Evidently the logarithmic
spacing should be followed and fortunately it is the log-
arithmic plotting of hydrogen ion concentration (in terms of
pH) which correctly depicts the fact that the difference between
1 x 10-9 and 2 x 10-9 may be as important for one set of
equilibria as the enormously greater difference between 1 X 10_J
and 2 X 10-2 is for another set of equilibria. This is revealed
in the charts on previous and subsequent pages.

Thus both convenience and the nature of the physical facts
compel us directly or indirectly to operate with some logarithmic
function of [H+].

It is unfortunate that a mode of expression so well adapted to the treat-
ment of various relations should conflict with a mental habit. [H+] repre-
sents the hydrogen ion concentration, the quantity usually thought of in
conversation when we speak of increases or decreases in acidity. pH varies
inversely as [H+]. This is confusing.

The normality mode of expression has historical priority and conse-
quently conventional force. Since there is a hydrogen ion concentration
for each hydroxyl ion concentration it became the custom, following Fried-
enthal (1904), to express both acidities and alkalinities in terms of [H+],
This gave a scale of one denomination and the meaning of "higher" and
of "lower" became firmly fixed. Now we meet the new scale with its direc-
tion reversed. The inconvenience is unquestionable and very largely be-
cause of it the pH scale has been criticized.

See the discussion in the Journal of the Washington Academy of Sciences
by Wherry and Adams (1921) and by Clark (1921). Wherry's (1919) chief
object is to establish a scale of convenient direction but in doing so he
gains a superficial advantage at the expense of several simple and very
important experimental and theoretical relations which he has not taken
into consideration.

SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA

In Chapter XIX there will be advanced a reason for adhering
to the use of the pH introduced by S0rensen; but at this point it
may be well to say that in both of the two chief methods of deter-
mining hydrogen ion concentration we encounter physical rela-
tions which make the errors proportional to pH rather than
to [H+]. Furthermore, pH is the more directly related to certain
electrode phenomena which are partially dependent upon hydro-
gen ion concentration and therefore pH is useful in dealing with
subjects outside the strict limits of hydrogen electrode
measurements.

The gross relation of [H+] to pH is shown in the following table.
See also table B appendix.

/ r

[H+]

io-°

lO"8

lO"1

10"9

10"2

10-io

io-»

10"11

io-«

10"12

io-«

10~13

io-«

10~14

10"T

The following symbols indicating hydrogen ion concentration

in normality are encountered in the literature [H+]; [H'

CH;h.

THE EFFECT OF DILUTION

A litre of normal acid becomes a fifth normal solution if diluted
to 5 litres; the hydrogen ion concentration may in many instances
be affected too little for the change to be detected by any but
refined methods. This apparent anomaly is frequently encoun-
tered and sometimes advantage of it is taken in the dilution of
solutions otherwise too dense optically for the application of the
indicator method. The effect of dilution upon the hydrogen ion
concentration of a solution may be briefly generalized by some
approximations.

38 THE DETERMINATION OF HYDROGEN IONS

Consider an acid of the type HA for the dissociation of which
we have the equilibrium equation:

[H+] X [A~] _
[HA]

If Ka is small there must obviously be a large reserve of undis-
sociated acid so long as the concentration of total acid is high.
As the solution is diluted this reserve dissociates to keep Ka
constant; but there is a readjustment of all components which
can be conveniently followed only by means of the simple algebraic
equation expressing the equilibrium condition.

If the acid alone is present in the solution we may assume that
[Ai = [H+]. Also if Sa = the total acid, [HA] = Sa - [H+].

Substituting these in the above equation and solving for [H+]
we have:

[H+] = WKaSa + ^--Ka (18)

* 4 2

When Ka is small in relation to S a

[H+] S VkK (19)

Compare the equation on page 19. On these assumptions the
hydrogen ion concentration should vary with dilution of the
solution (diminution of Sa) only as the square root of KaSa.

If there is present a salt of the acid we can apply the equation
derived on page 24 which shows that the hydrogen ion concen-
tration of a mixture of a weak acid and its highly dissociated salt
is determined approximately by the ratio of acid to salt. Since
dilution does not change the ratio, such a mixture should not suf-
fer a change of hydrogen ion concentration beyond the narrow
limits set by the approximate treatment with which this relation
was derived.

Therefore, except for solutions of high hydrogen ion concentra-
tion induced by the presence of unneutralized strong acids, the
hydrogen ion concentration should vary with dilution somewhere
between the zero change indicated by the last approximation and
the square root relation first indicated.

Such a conclusion takes no account of changes of equilibrium
which sometimes occur in colloidal solutions.

SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA

For bases and amphoteric electrolytes similar relations may be
deduced. One <jr two actual cases may be of interest.

S0rensen has given the following table of the pH values of dif-
ferent dilutions of asparagine and glycocoll.

MOLECULAR CONCEN-
TRATION OF GLY-
COCOLL

MOLECULAR CONCEN-
TRATION OF ASPAR-
AGINE

1.0

6.089

1.0

2.954

0.1

6.096

0.1

2.973

0.01

6.155

0.01

3.110

0.001

6.413

0.001

3.521

0.0001

6.782

0.0001

4.166

The dilution he're is ten-fold at each step, yet the increase in
pH is very small while the solutions are beween 1.0-0.01 M.

Walpole (1914) besides giving data on the hydrogen electrode
potentials of various dilutions of acetic acid and "standard ace-
tate," has determined the effect of a twenty-fold dilution of
various acetic acid-sodium acetate mixtures. The change of pH
on twenty-fold dilution of standard acetate is about 0.08 pH;
and of mixtures of acetic acid and sodium acetate which He on
the flat part of the curve the change of pH is of the same order

acetic acid

of magnitude. When the ratio — - -—reaches 19/1 the

sodium acetate

change is about 0.3 pH.

BUFFER ACTION

If we were to add to 1 liter of perfectly pure water of pH 7.0,
1 cc. of 0.01n HC1, the resulting solution would be about pH
5.0 and very toxic to many bacteria. If, on the other hand, we
were to add this same amount of acid to a liter of a standard beef
infusion medium of pH 7.0, the resulting change in pH would
be hardly appreciable. This power of certain solutions to resist
change in reaction was commented upon by Fernbach and Hubert
(1900) who likened the resistance of phosphate solutions to a
"tampon." The word was adopted by S0rensen (1909) and in
the German rendition of his paper it became " Puffer" and thence
the English "buffer." There has been some objection to this

40 THE DETERMINATION OF HYDROGEN IONS

word so applied but it now possesses a clear technical meaning and
I is generally used. By buffer action we mean t£e resistance ex-
hibited by a solution to change in pH through the addition or loss
of acid or alkali. This may be illustrated by titration curves such
as those shown in figures 4, 5 and 6. The construction of such
curves may be illustrated by the following example.

A 1 per cent solution of Witte peptone was found to have a
pH value of 6.87. To equal portions of the solution were added
successively increasing amounts of O.In lactic acid and the result-
ing pH was measured in each case. There were also added to
equal portions of the solution successively increasing amounts of
O.In NaOH and the resulting pH was measured in each case.
The pH values were then plotted on cross section paper as ordi-
nates against the amount of acid or alkali added in each case as
abscissas. This gave curve 1 shown in figure 4. The other
curve shown in this figure was constructed with data obtained
with a 5 per cent solution of Witte peptone. The curves of fig-
ures 5 and 6 were obtained in a similar way.

These curves illustrate the following points.
' Figure 4 shows that the buffer action of a solution is dependent
upon the concentration of the constituents. The 5 per cent solu-
tion is much more resistant to change in pH than the 1 per cent
solution. It will also be noticed that in either case the buffer
action is not the same at all points in the curve. In other words
the buffer action can not be expressed by a constant but must
be determined for each region of pH. This is illustrated even
more clearly by the titration curve for phosphoric acid (fig. 5).
At the point where the solution contains only tha:primary phos-
phate and again where it contains only the secondary phosphate
there is very little buffer effect indeed.

Furthermore the buffer action of a solution may not be due
entirely to the nature of the constituents titrated but also to. the
nature of the substance with which it is titrated. This point
may be illustrated by titrating a beef infusion medium in the one
case with hydrochloric acid and in the other case with lactic acid,
both of the same normality (see fig. 6). It will be seen that at
first the two curves are identical. As the region is approached
where the dissociation of the "weak" lactic acid is itself sup-
pressed because of the accumulation of lactate ions and the high

SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA

■ 5

•7

<*/

r»

)

c.c.

Fig. 4. Titration Curves of 1 Per Cent and 5 Per Cent Peptone

Ten cubic centimeters of peptone solution titrated with N/10 lactic acid
(to right) and with N/10 NaOH (to left).

i!£5

foyi

10
PH

KjHP

c.c.

100

150

Fig. 5. Titration Curve of Phosphoric Acid
Fifty cubic centimeters M/10 H3P04 titrated with N/10 KOH.

THE DETERMINATION OF HYDROGEN IONS

concentration of the hydrogen ions, further addition of this acid
has comparatively little effect. The strong hydrochloric acid
on the other hand continues to be effective until its dissociation,
too, at very high hydrogen ion concentrations is suppressed.

cue.

c.c.

Fig. 6. Titration Curves op a Beep Infusion Medium

One hundred cubic centimeters medium titrated with N/5 HC1 and with
N/5 lactic acid.

These examples will suffice to make it evident that the buffer
action of a solution is dependent upon the nature and the concen-
tration of the constituents, upon the pH region where the buffer
action is measured and upon the nature of the acid or alkali
added. To connect all these variables is a difficult problem.
Koppel and Spiro (1914) have attempted to do so but they have
necessarily had to leave out of consideration another factor. If

SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 43

there are present any bodies which tend to adsorb any of the con-
stituents of a solution which can affect the hydrogen ion concen-
tration of a solution, these bodies will tend to act as buffers or
will affect the buffer action of the solution. Henderson (1909) has
called attention to this and Bovie (1915) has shown in a very
interesting way the buffer action of charcoal. Since some culture
media or cultures and many of the solutions whose buffer action
must be studied for physiological purposes, contain undissolved or
colloidal material which may act in this way, it seems best to
consider buffer action in its broadest sense, and to express it by
the relative slopes of titration curves determined experimentally.
Further illustrations of titration curves of culture media will be
found in the papers of Clark (1915) and of Bovie (1915). Titra-
tion curves of some inorganic solutions will be found in a paper
by Hildebrand (1913).

The reader will have perceived the elementary theory under-
lying buffer action. The titration curve of phosphoric acid (fig. 5)
illustrates the principles discussed on previous pages. The titra-
tion curve of a "peptone" solution integrates as it were the effects
of acids, bases and ampholytes, in complex mixture.

Returning to figure 1 we see that along the flat portion of the
curve considerable alkali has to be added to produce much change
in pH. Conversely, the addition of a strong acid would not have
anywhere near the effect at this flat portion of the curve that it
would have near either end. Thus it is evident that a mixture of
a single acid and its salt will tend to stablize the pH of the solution
only within a certain narrow zone having vague boundaries.
Mixtures buffering the solution within such a pH zone are often
referred to as "regulator mixtures." They are of very great
value to the analyst and the physiological chemist in that they
furnish a means of stablizing the hydrogen ion concentration
within a predetermined zone. The middle point of this zone,
where the strongest buffer action is exerted, is determined approxi-
mately as shown on page 25 by the dissociation constant of the
acid or base concerned. Other things being equal the choice of
mixtures is thus revealed in a table of dissociation constants.
* [ More theoretical treatments of the subject are given in the
papers of Henderson (1909), S0rensen (1909), S0rensen (1912),
Michaelis (1914) and Koppel and Spiro (1914).

44 THE DETERMINATION OF HYDROGEN IONS

Unless a solution is buffered to some extent in some way, it is
almost impossible to make an accurate electrometric determina-
tion of the pH; and because of the influence of traces of carbon
dioxid and other acidic or basic contaminations such solutions
may be very unsuitable when used for physiological purposes.
Thus the failure to buffer against the effect of so-called neutral
salts which are not truly neutral may lead to gross error. In like
manner the failure to buffer has rendered physiologically unstable
certain so-called synthetic and supposedly stable culture media.

In the preparation of standard buffer mixtures it is of course, preferable
to use a high grade of water if accuracy is required but there is little need
of carrying this to an extreme. "Conductivity water" is sometimes speci-
fied for the preparation of special standards because the ordinary distilled
water of certain regions of the country is such that "distilled water" means
nothing. The exercise of judgment is advantageous.

The maintenance of "neutrality" by such solid reagents as calcium car-
bonate may be considered as a buffer action. It is very important to note
however that the use of calcium carbonate may become a grossly inefficient
procedure. To show its inefficiency the author has placed at the bottom of
a test tube a deep layer of very finely divided, freshly precipitated and well
washed calcium carbonate and overlaid this with cultures of bacteria and
molds in sugar media. Indicators show that unless the calcium carbonate
is frequently and thoroughly shaken with the medium only the solution
in direct contact with the calcium carbonate is neutralized. Molds may
develop an acidity as high as pH 2 within a few millimeters of the carbonate.

THE CONDUCT OF STRONG ELECTROLYTES

The relations set forth in the preceding pages, even in the
approximate form adopted to keep the distinctive lines of the
picture clear, afford in their experimental verification the best of
evidence that the theory of electrolytic dissociation is essentially
correct. That it is incomplete is shown when we turn to the
examination of the quantitative data for strong electrolytes —
acids such as hydrochloric and nitric and salts such as the simple
chlorides. For instance, if the conductance of a solution is
ascribed to the concentration and the mobilities of the ions, and
if the mobilities be considered constant at all dilutions, the con-
ductance data should satisfy the Ostwald dilution law and furnish

a dissociation constant. The Ostwald dilution law is q _ a)v = *

SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 45

where a is the degree of dissociation, v the dilution and k the
equilibrium constant which should be independent of the dilution;
a should be equal to the ratio of equivalent conductance at dilu-
tion v to equivalent conductance calculated for infinite dilution.
For potassium chloride, k varies from 0.049 at 1000 dilution to
0.541 at 10 dilution. The discrepancies with hydrochloric acid
are comparable.

The reader will recall that in the derivation of the equilibrium
constant (page 19) there was introduced an assumption full of
danger. The assumption was that the physical environment,
within which occur the reactions of dissociation and recombination,
remain constant. It has already been mentioned that a change
in temperature changes the equilibrium constant and that a
change in solvent produces a more profound effect. Now it is
not at all improbable that the presence of relatively large concen-
trations of ions and especially of the hydrogen or hydroxyl ions
constitutes an environment appreciably different from that of a
dilute solution. If so, we should hardly expect to find an equilib-
rium constant holding over a great range of concentration. Yet
it is by changing concentration that we expect to so alter the
distribution of "species" that we may demonstrate the "mass"
law experimentally.

But there are other possible difficulties. For instance, data
upon what may be called the structure of solutions, the mutual
influence of solvent and solute upon association of solvent mole-
cules, association of solute molecules and association of solvent
with solute are still hazy. Furthermore it is difficult to say
what degree of separation constitutes ionization as measured by
different methods. Therefore it is impossible to give rigidly
accurate values to the concentrations of active molecules. When,
therefore, it is stated that the anomalies of strong electrolytes
"disprove the mass law," it may be only a clumsy way of saying
that we do not know how to give the case an adequate test.

To give any adequate review of the present status of the prob-
lem would require undue space A most valuable review ap-
peared in the discussions which took place in the Faraday Society
and which are published in the December, 1919, number of the
Transactions. It is there made very evident that the " anomalies "
of strong electrolytes have been the bugbear of students of ioni-

46 THE DETERMINATION OP HYDROGEN IONS

zation, have stimulated most brilliant researches and promise to
be the starting point for new developments which will harmonize
the entire body of data.

There have been attempts to formulate the facts by means of
purely empirical equations; and then again the pendulum has
swung back to a faith that the original simple assumptions could
be satisfied if interfering factors were discovered and their numeri-
cal magnitudes introduced as corrections. More recently there has
come to the fore the "activity" concept of Lewis. This will be
mentioned again in Chapter XIX. This concept has attained con-
siderable success in systematizing the data; but whether it will
have an appeal universal enough to satisfy minds of the type of
Lord Kelvin, which reason not only in abstract terms but also
demand concrete models, remains to be seen.

When there occur in the development of a science such baffling
difficulties as have arisen in the case of "strong electrolytes,"
it is highly desirable to abandon both complex reasoning and end-
less corrections, if an entirely new basis can be found. This
statement will appear gratuitous or even foolish to those who are
so possessed with the idea of the complexity of aqueous solutions
that they admit no theory as sufficient that is not itself complex;
but the history of other developments has shown that in the face
of similar complexities a simple basis of reference has been found
and has won acceptance through its convenience.

Whatever may be the opinion of the reader he will doubtless
agree that we are in the midst of or at the beginning of a period
of transition, and that it is incumbent upon the experimenter to
keep his data as free as is convenient from confusions introduced
by tacit assumptions. In the following treatment of our subject
assumptions common to the age will remain, but at least they will
be more clearly recognized than if we straddled the issue that has
arisen. We shall therefore proceed with the concept of "con-
centration" as commonly used, since it is the more convenient
for elementary descriptive text. Finally in Chapter XIX we shall
redefine certain standards in such a way as to embody current
procedures and at the same time relieve the biochemist from
embarrassments due to the present state of flux.

Although free acidities of a magnitude that fall within the
grosser uncertainties of our knowledge of strong electrolytes are

SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 47

seldom met in physiological solutions, the whole system of pH
measurements is scaled from certain assumptions regarding the
now uncertain conduct of HC1 as will be shown in Chapter XIX.
Furthermore we have continually to deal with solutions contain-
ing salts whose conduct is so little understood that precise treat-
ment is impossible. This will appear in the so-called salt error of
indicators and the strange fact that the apparent hydrogen ion
concentration as determined with the hydrogen electrode may be
raised above the quantity of available acid present by the addi-
tion of sufficient salt. To deal with such questions without trac-
ing back through the subtleties of certain tacit assumptions is a
most pernicious practice. It seems wiser to admit at once that
certain of the more fundamental assumptions are too insecurely
based to provide any adequate systematic treatment at the present
time, and for this reason such questions as the salt error of indi-
cators will be given in the subsequent chapters what may at first
appear to be too brief a treatment. Experimentally the safest
procedure to follow whenever the conduct of strong electrolytes
enters into the determination of or the use of pH values is stand-
ardization of data.

Standardization of experimental data on the one hand and the
maintenance of the more simple concepts of the theory of electro-
lytic dissociation will then be the policy of the following treatment.

SUPPLEMENTARY REFERENCES

A few references on the conduct of "strong electrolytes" and the "activity"
concept. Arrhenius (1887, 1914), Beattie (1920), Bjerrum (1919),
Bronsted (1919-1922), Ebert (1921,)* Ferguson (1916), Ferguson-
France (1921), Getman (1920), Ghosh (1921), Harkins (1920), Harned
(1916, 1920, 1922), Hill (1921), Jahn (1900), Kendall (1921, 1922),
Kraus (1920, 1921), Lapworth (1915), Lewis (1907-1922), Linhart (1917,
1919), Noyes (1907), Noyes-Maclnnes (1920), Maclnnes (1919),
Rabinowitsch (1921), Stern (1922). Symposium on theory of electro-
lytic dissociation Trans. Faraday Society 15, 1-178, Dec. 1919.

pH calculator. Klopsteg (1921).

pH tables and graphs. Appendix table b. Matula (1916), Roaf (1920),
Schmidt-Hoagland (1919), Symes (1916).

* Contains extensive review.

CHAPTER III

Outline op a Colorimetric Method

Acidimetric-alkalimetric indicators are substances, the colors
of which correlate with the hydrogen ion concentrations of the
i aqueous solutions in which they are dissolved.

For each indicator there is a characteristic pH zone. On the
acid side of this zone the indicator is completely transformed into
its "acid color" and on the alkaline side of this zone the indicator
is completely transformed into its "alkaline color." Within the
characteristic pH zone there may be observed different proportions
of the acid and alkaline colors.

In ordinary titrations conditions are so chosen that when the
"end-point" of the titration is reached the pH of the solution
passes suddenly through the whole range of the indicator's color-
change. The intermediate stages, if observed, are not emphasized.
The intermediate colors, however, are the important ones for the
present purpose. They can be maintained with buffer solutions;
and, being characteristic at definite pH values, they can be used
to estimate the pH of tested solutions by a system of comparison
with standards. To distinguish the stabilized degree of color
transformation from the changing color observed during a titra-
. tion, we shall adopt S0rensen's term and speak of the virage of
an indicator when referring to a particular, stabilized degree of
color transformation.

For reasons which will be given in Chapter IV the characteristic
pH zone, within which differences of virage may be observed, is
comparatively narrow. It is therefore necessary to have a series
of indicators, the zones of which overlap (see table on page 80).
Then if an indicator is found to be transformed completely to its
acid color by a solution under test, the indicator next in the series
is tried and so on until there is found the indicator which is trans-
formed by the solution 'to an intermediate virage. It is then
known that the solution has a pH value within the limits char-
acteristic of the indicator used.

For some purposes it is sufficient to know the approximate pH
and this may be estimated from the degree of color transformation

OUTLINE OF COLORIMETRIC METHOD 49

induced in the indicator. It is a simple matter, however, to take
the first step toward accuracy. This is done as follows.

There have been determined by hydrogen-electrode methods
the pH values of definite buffer solutions such as mixtures of
KH2PO4 and Na2HP04. Series of such solutions and the details
of their preparation are described in Chapter VI. By adding
definite quantities of an indicator to definite volumes of these
standard solutions a series of color standards is easily prepared.
With these standards the color of the tested solution can be
compared. For instance, suppose that the preliminary test of a
given solution has shown that it transforms the indicator phenol
red neither to a full red nor to a bright yellow but that the pro-
portion of red is low. Previous experience has impressed the fact
that such a virage with phenol red indicates the solution to be near
pH 7.0. See the color chart. Therefore, one employs those
standard buffer solutions giving pH values near 7.0. To a series
Df uniform test tubes is added seriatim 10 cc. of each of the
standard phosphate solutions described in Chapter VI. To each
:ube is added five drops of phenol red solution. On mixing there
vill be observed a graded series of virages and perhaps three of
;hem will be recognized at once to have nearly the same color as
10 cc. of the tested solution mixed with 5 drops of the same indi-
;ator solution. When closer inspection shows where the color-
natch occurs, the standard with its known pH value and the
ested solution are supposed to have the same pH value. As in
his example, it is always necessary to make comparisons between
,ike concentrations of indicator viewed through equal depths of
s olution.

Anerrorjnay be made if the standard and tested solutions /
i liffer much in total salt concentration, or if the tested solution
i ontains much protein, or if an unreliable indicator is used. But
\ fe shall have to deal with these and other difficulties in subse-
( uent chapters.

When one is familiar with the virages of the indicators at
] nown pH values very fair estimations may be made without the
i id of the standards; but there is no way as satisfactory as the
{ stting up of the standards for the establishment of a correct
i npression of the relations of the various indicators on the pH

50 THE DETERMINATION OF HYDROGEN IONS

scale. On the other hand, the author has discovered in his
conversations that there are a great many investigators who
would like to use indicators for the occasional rough measurement
of pH but who are discouraged by a pressure of work which pre-
vents them from taking the time to carefully prepare the standard
solutions. To furnish such investigators with a demonstration of
the general relations of the various indicators and to furnish
rough standards the attempt has been made in figure 8, to repro-
duce the colors. The colors of standard buffer solutions con-
taining definite quantities of the several indicators were reproduced
very faithfully by Mr. Max Broedel of the Johns Hopkins Medical
School. It must be remembered, however, that in undertaking a
second reproduction by means of the printer's art the publishers
are to be commended for their courage and are not to be held
responsible for the inadequacy of the result. Aside from the
inherent difficulty in freeing a printed color from the effect of the
vehicle, there remains the utter impossibility of reproducing upon
paper the exact virage observed in a liquid solution. The funda-
mental phenomena are quantitatively very different in the two
cases. Therefore the user of the chart of colors will have to use
discretion and some imagination. If he does not attempt to
make the reproductions take the place of the standards he should
find them useful for class room demonstrations, for refreshing the
memory and for rough standards.1

In each case the colors were reproduced from tubes 16 mm.
internal diameter containing 10 cc. standard buffer solution.
The quantities of indicator solution added in each case were as
follows: Thymol blue, acid range (T. B. acid range) 1 cc. 0.04
per cent solution. Brom phenol blue (B. P. B.) 0.5 cc. 0.04 per
cent solution. Methyl red (M. R.) 0.3 cc. 0.02 per cent solution.
Brom cresol purple (B. C. P.) 0.5 cc. 0.04 per cent solution. Brom
thymol blue (B. T. B.) 0.5 cc. 0.04 per cent solution. Phenol red
(P. R.) 0.5 cc. 0.02 per cent solution. Cresol red (C. R.) 0.5 cc.
0.02 per cent solution. Thymol blue (T. B.) 0.5 cc. 0.04 per cent
solution.

1 Separates of the color chart may be obtained from the publisher.

Dr. Barnett Cohen of the Hygienic Laboratory has recently
(Public Health Reports, U. S. P. H. S., 38, 199, 1923) synthe-
sized the following new sulfonphthalein. Brom cresol green
covers the range of methyl red. Salt and protein errors have
not yet been determined.

CHEMICAL, NAME

8CGGESTED COMMON NAME

APPARENT

DISSOCIATION

CONSTANT

RANGE

m-Cresol sulfonphthalein

Meta cresol purple

2.8 X lO"2
5.0 X 10~9

0.5-2.5
7.6-9.2

Dibromo-dichloro-phenol sul-
fonphthalein
Tetra bromo-m-cresol sulfon-

Brom-chlor phenol

blue
Brom cresol green

7.9 X lO"6
1.0 X 10~5

3.2-4.8
4.0-5.6

phthalein

Dichloro-phenol sulfonphtha-
lein

Dibromo-phenol sulfonphtha-
lein

Chlor phenol red
Brom phenol red

8.9 X 10~7
4.5 X 10~7

5.0-6.6
5.4-7.0

OUTLINE OF COLORIMETRIC METHOD 51

The ranges of pH covered by the^ several indicators in the
color chart are:

T. B. (acid range), Thymol blue 1.2-2.8

B. P. B., Brom phenol blue 3.0-4.6

M. R., Methyl red 4.4-6.0

B. C. P., Brom cresol purple 5.4-7.0

B. T. B., Brom thymol blue 6.0-7.6

P. R., Phenol red 6.6-8.2

C. R., Cresol red 7.2-8.8

T. B., Thymol blue 8.2-9.8

For class-room work it is advantageous to show the position
of the several indicators on the pH scale by relining each series
so that corresponding pH values overlap.

One requirement for the colorimetric method is a set of indi-
cators selected for their relative freedom from the so-called pro-
tein and salt errors and for their brilliancy. Beside the brilliant
and reliable selection of Clark and Lubs there is the care-
fully studied selection of S0rensen given on page 78 with S0rensen's
summary of properties on page 79.

There are also required standard buffer solutions whose pH
values are established from hydrogen electrode measurements.
It is in the preparation of these standards that the greater part
of the labor of the colorimetric method is involved ; but, once the
stock solutions are carefully made, the preparation of the mix-
tures is a simple matter. If only the pH range 5.2 to 8.0 is
necessary, the S0rensen mixtures of primary and secondary phos-
phates are the more convenient. If a wider range is desired the
system tabulated on pages 106 to 107 is recommended.

For precise measurements there are required control by hydro-
gen electrode measurements and constant watchfulness for the
several sources of error noted in following chapters. Approximate
methods are described in Chapter VIII.

In figure 7 are shown several pieces of equipment useful in
colorimetric work. Beginning at the left is, first, a sample of
a litre bottle used for holding the standard stock solutions, such
as M/5 KH Phthalate, which are not seriously affected by expo-
sure to the carbon dioxide of the laboratory air. In Clark and
Lubs' series of standards (see page 99) there are required four
such bottles. In this same series there is required a container for

C3 -

6 f

OUTLINE OF COLORIMETRIC METHOD 53

standard M/5 NaOH. This should be a paraffined bottle with
calibrated burette and soda-lime guard-tubes attached.

In figure 7 there is next shown a comparator whose construc-
tion is given on page 70. This is used in comparing turbid or
colored solutions with the standards. When the turbidity of a
tested solution brings into evidence the dichromatism of an indi-
cator as described on page 65, the comparator is used with the
light screen shown at the back of figure 7 and described on page 67.

For ordinary colorimetric comparisons the test tube rack shown
in the figure is very useful. The holders are the clips sold at
stationers for holding rubber stamps. Two forms of dropping
bottle are next shown and, finally, at the right, two paraffined
bottles for alkaline standards and two acid resistant bottles for
acid solution. Of such bottles there are required for the series
of standards given on pages 106-107 fifty-one bottles and the same
number of 10 cc. pipettes. The range of pH thus covered is wider
than that called for in special investigations. The pipettes may
have their tips broken to allow quicker delivery of solution with-
out serious violation of volume requirements. S0rensen's stand-
ards, pages 111-114, are designed so that individual 10 cc. samples
are made up as required. Larger quantities such as are specified
in table 21 provide for the occasional test.

CHAPTER IV

Theory of Indicators
Les proprUUs des corps sont les proprUUs des nombres.—T>E Chancotjrtois.

Indicator theory is a cross-roads where the cultivators of
distinct fields of science meet. Here comes the organic chemist
with analyses of plant and animal products, structural formulas
of synthetic dyes, tautomers and chromophores. Here comes the
physico-chemist with formulations of electrolytic and tautomeric
equilibria. Here comes the physicist with the theory of color and
the instruments of light analysis. And perhaps there will meet
here the psychologist bringing a clearer description of the sub-
jective aspect. As a confluence of trade routes may determine the
growth of a city so the confluence of many specialties may some-
time lead to a great community of interest where the cross-roads
of indicator theory once lay. Indicators themselves are not
particularly unique except that they compel the attention of the
eye. Through this we are made aware of phenomena of wide
occurrence.

According to the inclination of a reviewer one or another of
the manifold aspects of indicator theory might be emphasized.
"' We must choose that which is useful to the purpose at hand and
for the sake of a necessary brevity we must try to include only
so much as will contribute toward an intelligent use of indicators
as tools for the determination of hydrogen ion concentration.

In the first place it may be said that the customary manner of
using indicators is merely a method of comparison involving little
if any theory. The conduct of an indicator may be, and generally
is, ."calibrated" by means of hydrogen electrode measurements.
It is well to emphasize this uninspiring, matter-of-fact aspect
because it will remind us that with so much of the fundamental
theory at hand the employment of theory may lead to a wider
usefulness of the instruments thus far treated empirically. But
before this can be done important relationships must be ex-
pressed definitely in numerical data. How this can be done is
the immediate problem before us.

THEORY OF INDICATORS

The first consistent attempt to bring the conduct of indicators
into relation with electrolytic dissociation was that of Ostwald
(1891). .He assumed that indicators are acids or bases the undis-
sociated molecules of which have a color different from that of their
dissociation products. If this be so, it is evident that the color

TABLE 4
Approximate apparent dissociation constants of indicators

Phenol sulfon phthalein

o-Cresol sulfon phthalein

Thymol sulfon phthalein

Carvacrol sulfon phthalein

a-Nap&hol sulfon phthalein

Tetra bromo phenol sulfon phthalein.
Di bromo o-cresol sulfon phthalein. . .

Di bromo thymol sulfon phthalein

Phenol phthalein

o-Cresol phthalein

a-Naphthol phthalein

Methyl red

Ethyl red

Propyl red

Thymol sulfon phthalein (acid range) .

.2 X 10"
.0 X 10"

10"
10"
10"

io-

10"

.2 X

0 X

3 X

9 X

0 X

0 X io-
0 X io-

0 X 10"

0 X io-

9 X 10-

0 X io-

0 X 10"

o x io-

pKa

7.9

8.3

8.9

9.0

8.2

4.1

6.3

7.0

9.7*

9.4

8.4

5. If

5.4

5.4f

1.7

* This value is identical with Rosenstein's (1912).

t In the table published in the Journal of the Washington Academy,
vol. vi, p. 485, these values for methyl red and propyl red were erroneously
interchanged.

Tizard (1910) gives Ka = 1.05 X 10"6 or pK - 4.98 for methyl red
considered as an acid.

of an indicator should change with the pH of a solution. exactly
as the dissociation curves described in Chapter I. If, for in-
stance, the indicator is an acid, colorless in the undissociated
form, but colored when dissociated as an anion, then the change
of color with the hydrogen ion concentration should conform to
the equation:

Ka + [H+]

where Ka is the dissociation constant of the acid indicator and
a is the degree of dissociation. Assuming then that such a rela-

THE DETERMINATION OF HYDROGEN IONS

tion does hold, let us determine Ka for a series of indicators in
the following way.

From the above equation when « = §, Ka = [H+]. That is,
at a hydrogen ion concentration corresponding numerically to the
dissociation constant, the acid is half dissociated. At such a
hydrogen ion concentration a colorless-to-red indicator, such as
phenolphthalein, should show half the available color; and a
yellow-to-red indicator, such as phenol red, should show the half-
yellow, half-red state. We can match the half way state of this
first solution by superimposing two solutions each of a depth
equal to the first, if we have in one of the superimposed solutions
only the yellow form and in the other only the red form, each
concentration equaling half the concentration in the first solution.
Such an arrangement is shown diagraphically in the following
figure :

Alkaline solution (full
red) 5 drops indicator

Known pH standard
10 drops indicator

Acid solution (full yel-
low) 5 drops indicator

Water blank

We may not know at the beginning at what pH the half trans-
formation may occur, so we vary the pH of the standard solution
until a match with our superimposed solutions does occur. Then
we have found, presumably, the hydrogen ion concentration the
numerical value of which is the dissociation constant of the
indicator. Values so obtained by Clark and Lubs (1917) are given
in table 4.

THEORY OF INDICATORS 57

< As indicated in Chapter I the determination of the dissociation
curve, or of the half transformation point, does not tell us whether
we are dealing with the dissociation curve of an acid or the disso-
ciation-residue curve of a base or vice versa. Thus methyl red
is treated in table 4 as an acid and plotted in figure 9 as if the
color were associated with the undissociated form. Methyl red
however could be treated as a base.
Just as it is convenient to deal with a logarithmic function of

[H+] so the dissociation constants can be used in the form log —

This can be designated pKa.

Gillespie (1920) gives somewhat different values but, since the
method used in each case was approximate, the table given above,
as it is^found in the paper by Clark and Lubs (1917) will do for
purposes of illustration. With the aid of the approximately
determined apparent dissociation constants we are enabled to
plot the curves shown in figure 9, which reveal graphically the
relationships of the various indicators in the series we shall dis-
cuss. This figure shows at a glance that an indicator of the
simple type we have assumed has no appreciable dissociation and
consequently exists in only one colored form at pH values begin-
ning about 2 points below the half transformation point, while at
the same distance above this point the indicator is completely
dissociated and exists only in its second form. Between these
limits the color changes may be observed. The useful range of
such an indicator is far less than 4 pH units for optical reasons
which will be discussed later.

The illustration (fig. 9) will show how in choosing a set of indi-
cators it is advantageous to include a sufficient number, if reli-
able indicators can be found, so that their ranges overlap. It
shows that each of the indicators, when considered to be of the
simple type we have assumed, has an equal range. It also shows
that the half transformation point of each indicator occurs nearer
one end of the useful range, the useful range being indicated by
the shaded part of the curve. This aspect will be discussed later.

It is evident that if the actual color change of an indicator varied
with pH in accordance with a curve such as those in figure 9,
and if the true dissociation constant were accurately known, then
the hydrogen ion concentration of a solution could be determined

<^-

GASTB1 C

JUICS

YEAST
LIMIT

WIKES

CASEIN ISO-
ELECTRIC PT.

i^L

X/C

•*r"

*s,<i*

SEA
WATER

^s^

10 ^

Z$ „ SO 7S

% DISSOCIATION

1^10 HCJ

B.PARA TYPHI ACCL.

B. TYPHI Afl«L.
B.COLI LIMIT
PBEUMOCOCOTS AGCL.

M/2

yiO MH4OH

too

Fia. 9. Indicator Curves and Significant pH Values. Shading
Indicates Useful Range

THEORY OF INDICATORS 59

by finding the percentage transformation induced in the indicator.
Indeed the dissociation constants of some few indicators have
been determined with sufficient accuracy to permit the use of
this method when the proper means of determining the color
intensities are used. This will be discussed in Chapter VIII. R

We have been assuming that thejtheory of indicators may be
treated in the simple manner originally outlined by Ostwald
(1891). In his theory it was assumed that the anion of an indi-
cator acid, for instance, has a color different from that of the
undissociated molecule. This assumption if unmodified does not
harmonize with what is known. Researches in the phenomena of
jtautomerism have shown that when a change in color is observed
in an indicator solution the change is associated with the forma-
tion of a new substance which is generally a molecular rearrange-
ment or so-called "tautomer" of the old. If this color change is
associated with the transformation of one substance into another,
how is it that it seems to be controlled by the hydrogen ion con-
centration of the solution? As Steiglitz (1903) and others have
pointed out, it is the state of these compounds, their existence in
a dissociated or undissociated condition, which determines the
stability of any one form.

The method of dealing with the tautomeric relations of indi-
cators is shown by the following quotation from Noyes (1910) :

We may derive a general expression (as has previously been done by
Acree, 1907) for the equilibrium-relations of any pair of tautomeric acids
and their ions. The three fundamental equilibrium equations are as
follows:

eaaci.K/. (20) (H+) aid - K* . (21)

(HIn') " ( (HIn") K »» **"

2S2-&- (22)
(HInO Kt' (22j

Multiplying (21) bv (22), adding (20) to the product, and substituting in

♦ t ,ttt rx -, , (HlnQ + (HIn'

tor for (HIn ) its value —

1 + KT

(H+) [(In'") + (In'")] K', + K", K,

fTTTnM -I- fTTTn'M

the denominator for (HIn') its value — — — given by (22), we get

1 + KT

(HInO •+ (HIn") 1 + K,

= KIA (23)

If the indicator is a base existing as the two tautomeric substances
fn'OH and In"OH, having ionization constants K'r and K"i and a tau-
tomer constant KT denned by equations analogous to (20), (21) and (22), the

60 THE DETERMINATION OF HYDROGEN IONS

general expression for the equilibrium between the ionized bases and their
ions is:

(OH") [(In'+) + (Iny+)] -K'x+K'xKt

(In' OH) + (In'OH) 1 + KT

= KIB (24)

In these expressions a single constant KIA or KIB has been introduced in
place of the function of the three constants K'x, K"i, and KT . . . •
The constant so calculated for a pair of tautomeric acids or bases can evi-
dently be substituted for the ionization constant of an ordinary (non tau-
tomeric) acid in any derived expression, provided the sum of the two ion
concentrations and the sum of the two acid or base concentrations are quan-
tities that are to be known or are to be calculated.

If then in equation (23) we substitute (In-) for [(In'~~) -+- (In"~)] and
(HIn) for [(HIn') + (HIn")] we have:

(HIn) " KlA (25)

Applying to Noyes' equation (25) the derivation given on page 25
we have

KIA + (H+)'

From this we may plot the curves of figure 9. Such curves will
then represent the color transformations when and only when
(In-) is substantially equal to (In'-) or to (In"-), whichever
tautomer is associated with the color. The most probable expla-
nation of the fact that such curves do represent very closely the
color transformations in certain instances is that KT (see equation
(23)) is so small that the dissociation brought about by salt for-
mation leaves (In-) dominant.

In other words it is, after all, the degree of dissociation, as
determined by the hydrogen ion concentration, that determines
which tautomer predominates. Therefore, consideration of the
tautomeric equilibria only modifies the original Ostwald treat-
ment to this extent : the true dissociation constant is a function of
the several equilibrium and ionization constants involving the
different tautomers and must be replaced by what Acree calls the
"total affinity constant," or by what Noyes calls the "apparent
dissociation constant," when it is desired to show directly how
the color depends upon the hydrogen ion concentration.

Many indicators are poly-acidic or poly-basic and will not
rigidly conform to the treatment for a simple monovalent acid
such as we have described. Phenolphthalein, for instance, as
was shown by Acree (1908) and by Wegscheider (1908) must be

THEORY OF INDICATORS

considered as poly-acidic. The proper equations to apply
in this case have been given by Acree (1907, 1908) and also by
Wegscheider (1908, 1915). According to Acree and his students
(Acree, 1908) (Acree and Slagle, 1909) the chief color change in
phenolphthalein is associated with the presence of a quinone
group and with the ionization of one of the phenol groups. In
the sulfon phthalein series of indicators Acree and his students
(White, 1915, and White and Acree, 1918) have found much the
same sort of condition.

In the sulfon phthalein series, however, certain unique proper-
ties described by Lubs and Acree (1916) make the series eminently
suited for experimental demonstration of the seat of color change.

In the sulfon phthalein group of indicators we have to deal
with poly-acids; but as Acree has shown, the dissociation con-
stant of the strong sulfonic acid group is so very much greater
than that of the weak phenolic group, with which the principal
color change is associated, that there is no serious interference.
As shown in Chapter I we may, therefore, plot the curves for the
chief color-changes as if we were dealing with monobasic acids.

The structures of all the sulfon phthaleins are analogous to
that of phenol sulfon phthalein (phenol red) whose various tau-
:omers are given by Lubs and Acree (1916) in the following
scheme :

C6H4OH
I
:6H4-C(C6H4OH)2 -» C6H4-C-C6H4OK -* C6H4-C(C6H4OK)2
II' II II

302 - O S02 - O S02 - O

A colorless B colorless C colorless

C6H4OH

I
^6H4 — C : CeEU : O
I

302-OH
) slightly colored

C6H4OH

I
CeH4 — C : CeH4 : 0
I

S020- + H+
E slightly colored

C6H40-K+
l I I
CeH4 — C : CeH4 : 0

C6H4OH

I
— ► CeH4 — C '. C6H4 ! O
I

S020- + K+
F slightly colored

i ■

C6H40-+K+
I
CeH4 — C i CeH4 lO

S020" + K+
H deeply colored

S020- + K+
G deeply colored

62 THE DETERMINATION OF HYDROGEN IONS

The colorless lactoid A by reason of the strong tendency of
the sulfonic acid group to ionize goes over into the quinoid struc-
tures illustrated in the second line which are slightly colored
yellow. It is the transformation of F to G and H, the ionization
of the phenolic group forming a quinone-phenolate structure
which correlates with the intense red color of phenol sulfon
phthalein (phenol red).

Just as the discovery of tautomerism seemed at first to discredit
the original form of the Ostwald theory of color change, so it is
now realized that a mere change in structure is of itself quite
inadequate to account for the change in the light absorption upon
which the color of a solution depends. Light is an electro-
magnetic phenomenon and the absorption of the energy in any
particular train of light is undoubtedly due to the resonance of
electrons. Thus the direct connection between light absorption
and molecular structure will be found in the relation of molecular
structure to the distribution and freedom of the component
electrons. It is in this direction that Baly (1915) believes a
satisfying theory of the colors of dyes will be found. Although
Baly has called attention to difficulties in the correlation of colors
with tautomeric changes there seems to be no inherent reason
why tautomerism, alteration of the fields of force within the
molecule, electrolytic ionization and color should not be corre-
lated. The original Ostwald theory may yet prove to be essen-
tially correct in that the charging of a molecule by ionization
should cause a redistribution of the fields of force. Whether or
not a molecular rearrangement or absorption of a particular train
of visible light follows may well depend upon particular cir-
cumstances. But of course all this is left to the future and to
quantitative data.

OPTICAL ASPECTS

While the color changes of indicators are correlated with molec-
ular rearrangements controlled by hydrogen ion concentrations,
it should not be forgotten that the phenomena observed are opti-
cal and tnat no theory of indicators can be considered complete
enough for practical purposes which fails to recognize this. As
ordinarily observed in laboratory vessels the color observed

THEORY OF INDICATORS 63

is due to a somewhat complex set of phenomena. It is unfortu-
nate that we have no adequate treatment of the subject which
at the same time embraces electrolytic dissociation, tautomerism
and the optical phenomena in a manner directly available in the
practical application of indicators. The simultaneous treatment
of these various aspects is necessary before we can feel quite
sure of our ground when dealing with discrepancies often
observed in the comparison of colorimetric and electrometric
measurements of biological fluids.

Let us first consider the range of an indicator as it is determined
by the differentiating power of the eye. An approximate treat-
ment of this is all that will be attempted.

Using equation (10), cf. page 26:

1 a

pH = log — + log

K (1 - a)

we find on differentiation that the rate of increase in a with
increase of pH is:

d(PH)
When

a (1 — a).

- 0, a - i<

d(pH)2 2

In other words the maximum rate of increase in dissociation is at
the half transformation point. This fixes a reference point when
indicators are to be employed in distinguishing differences in pH.
The question now arises whether or not this is the central point
oi the optimal conditions for differentiation of pH values. It
may be said at once that it is not, because the eye has not only
to detect differences but also to resolve these differences from the
3olor already present. Experience shows that the point of maxi-
mum rate of increase in a is near one limit of the useful range and
'hat this range lies on the side of lower color. Thus, in
:he case of the one-color indicator phenolphthalein, the useful
?one lies between about 8.4 and 9.8 instead of being cen-
tred at 9.7 which corresponds with the point of half-transforma-
ion. In the case of a two-color indicator such as phenol red the

64 THE DETERMINATION OF HYDROGEN IONS

same reasoning holds, because the eye instinctively fixes upon the
very dominant red. With other two-color indicators the principle
holds except when there is no very great difference in the com-
mand upon the attention by one or the other color.

It should be mentioned however that these more or less empiri-
cal relations are observed in comparing virages at equal incre-
ments of pH when the indicator concentration is adjusted to
emphasize the differences among the less intensely colored tubes.
By suitable dilution of the indicator the differences among the
tubes having the higher percentage color may be emphasized
and the useful range of the indicator slightly extended. In prac-
tice this is a procedure which requires care for it is easy to be-
come confused when dealing with different concentrations of the
same indicator.

The fixing of the lower limit of usefulness of a given indicator
involves another factor. There is the question of the total
indicator which may be brought into action. A dilute solution
of phenolphthalein may appear quite colorless at pH 8.4 while
a much stronger solution will show a distinct color which would
permit distinguishing 8.2 from 8.4. But the concentration is
limited by the solubility of the indicator and therefore must be
taken into consideration. In short there is no basis upon which
to fix definite limits to the pH range of a given indicator, and
those limits which are given must be considered to be arbitrary.
On the other hand the. apparent dissociation curve is quite
definitive; and were it not for the greater convenience of the
"range of usefulness" it would be preferable to define the charac-
teristics of an indicator in terms of its apparent dissociation
constant.

We ordinarily speak of color as it if were an entity. As a mat-
ter of fact the color exhibited by an indicator in solution is due to
the selective absorption of certain frequencies of the incident
light. This results in the partial or complete blocking off of the
light in one or more regions of the spectrum, as may be seen by
the dark band or bands which appear when the solution is viewed
through a spectroscope. The transmitted light instead of being
of the continuous spectrum which blends to subjective white is
made up of the unaffected wave lengths and of those wave trains
the intensities of which have been reduced to a greater or lesser

THEORY OF INDICATORS 65

extent. The resultant subjective color must be distinguished from
the color associated with a definite region of the spectrum.

We come now to the consideration of a phenomenon which is
undoubtedly exhibited with all indicators but which is generally
not noticed except in special instances. In some of these instances
it becomes of great importance and may lead to serious error unless
recognized. The phenomenon we speak of is the dichromatism
exhibited, for instance, by solutions of brom phenol blue. Solu-
tions of this indicator appear blue when viewed in thin layers but
red in deep layers. The explanation is as follows : The dominant
absorption band of the alkaline solution is in the yellow and the
green, so that the transmitted light is composed almost entirely
of the red and blue. The incident light has an intensity which
we may call I. After transmission through unit thickness of
solution some of the light has been absorbed and the intensity
becomes la, where a is a fraction — the transmission coefficient —
which depends upon the nature of the absorbing medium and the
wave length of the light. After traversing thickness e the inten-
sity becomes Iae. Now the transmitted blue is Ib«b€ and the
transmitted red Irare. We do not happen to know what the
actual values are, but, merely to illustrate the principle, let us1
assume first that the intensity of the incident blue is 100 and of the
red 30 and that a^ = 0.5 and at = 0.8.

For e = 1, Ibab* = 50 and Irar6 = 24. Hence blue greater than
red.

For' e = 10, Ibflb6 = 0.01 and Irare = 0.30. Hence blue less than
red.

This example indicates that the solution may appear blue
when viewed through thin layers while it may appear red when
viewed through thick layers.

If we change the relative intensities of the incident red and blue
we can change the color of a given thickness of solution. If in
the above example we reversed the intensities of the incident red
and blue, then,

For e = 1, Ibflbe = 15 and Irar€ = 80, or red greater than blue.

This is essentially what happens when we carry the solution
•rom daylight, rich in blue, to the light of an electric carbon fila-

66 THE DETERMINATION OF HYDROGEN IONS

ment lamp, poor in blue. The solution which appears blue in
daylight appears red in the electric light.

The practical importance of recognizing the nature of this
phenomenon may be illustrated in the following way. Suppose
we have a solution rich in suspended material such as bacterial
cells, and that we wish to determine its pH value by using brom
phenol blue. If we view such a solution in deep layers very little
of the light incident at the bottom reaches the eye. A large
proportion of the light which does reach the eye is that which
has entered from the side, has been reflected by the suspended
particles, and has traversed only a relatively thin section of the
solution. In such a solution then, if it is of the proper pH, brom
phenol blue will appear blue, while in a clear comparison solution
of the same pH the indicator appears red or purple if the tube is
viewed lengthwise. A comparison is therefore impossible under
these conditions. If, however, we view the two solutions in rela-
tively thin layers, as from the side of a test tube, they will appear
more nearly comparable. There will still remain, however, a
clearly recognizable difference in the quality of the color which
serves as a warning that the two solutions are not being compared
under proper conditions.

Now a change in the quality of the light in which the turbid
and the clear solutions are compared will, of course, not avert
one fundamental difficulty — a difference in effective path; but a
proper change in the quality of the light can eliminate the di-
chromatism and free the eye from one source of confusion. In
the case at hand we might eliminate either the red or the blue.
Which had best be eliminated is a question which can not be
answered properly until we have before us the necessary spectro-
metric measurements. Nevertheless the following observations
made with a small hand spectroscope, and the deductions there-
from may prove to be illuminating.

i The chief absorption bands of brom phenol blue solutions occur
in the yellow-green range and in the blue. In alkaline solutions
the band in the blue disappears while that in the yellow widens
into the green. As the solution is made more acid the band in
the blue appears, shutting off the transmitted blue, while that in
the yellow-green contracts, permitting the passage of the green.
Our light source then should be such that at least one of these

THEORY OF INDICATORS 67

changes may become apparent, and at the same time either the
blue or red must be eliminated. The light of the mercury arc
fulfills these conditions. It is relatively poor in red and it emits
yellow, green and blue fines where the shifts in the absorption
bands of brom phenol blue occur. Since the mercury arc is not
generally available we have devised a light source to fulfill the
alternative condition, namely, one which will permit observation
of the contrasts due to the shift in the yellow-green band1 and
which at the same time is free from blue. Such a source is found
in electric light from which the blue is screened by a translucent
paper painted with a yellow, acid solution of phenol red. One dis-
advantage of such a screen is that the red transmitted through
it is so dominant that it obscures the contrasts which are due
to the shifting of the yellow-green absorption band. Nevertheless,
such a screen has proved useful in pH determinations with brom
phenol blue and particularly useful with brom cresol purple.
In either case it is most useful in the more acid ranges covered
by these indicators.

The device consists of an ordinary box of convenient size in
which are mounted three or four large electric lights (e.g., 30 cp.
3arbon filaments). A piece of "tin" serves as reflector. The box
nay be fined with asbestos board. A piece of glass, cut to fit the
Dox, is held in place on one side by the asbestos lining and on the
)ther by a few tacks. This glass serves only to protect the screen
md is not essential. The screen is made from translucent paper
mown to draughtsmen as "Economy" tracing paper. It is
stretched across the open side of the box and painted with a
solution consisting of 5 cc. of 0.6 per cent phenol red and 5 cc.
)f M/5 KH2P04 (stock, standard phosphate solution) . While the
)aper is wet it is stretched and pinned to the box with thumb
acks. This arrangement may be constructed in a very short
ime and will be found very helpful in many cases. It should be
ised in a dark room or, if such a room is not available, exterior
ight may be shut off with a photographer's black cloth.

While considering light sources we may call attention to the
: act that all the sulfon phthalein indicators may be used in elec-

1 This should not be confused with the changes in "subjective color."
~_ n the screened light no participation of transmitted green will be detected
1 y the unaided eye.

68 THE DETERMINATION OF HYDROGEN IONS

trie light, although brom thymol blue and thymol blue are not
well adapted for use in light poor in blue. Doubtless a more
thorough investigation of the absorption spectra of the sulfon
phthalein indicators will make it possible to devise light sources
which will materially increase their efficiency.

So far as we have been able to detect with instruments at hand,
the absorption spectra of all the indicators of the sulfon phthalein
series are such that the appearance of dichromatism must be
expected under certain conditions. It will be observed with phe-
nol red in light relatively poor in red and rich in blue, for example,
the light of a mercury arc; and with thymol blue in light relatively
poor in blue and rich in red for example, ordinary electric light.

When the colorimeter is employed in the study of colored solu-
tions the applicability of Beer's law is assumed. This may be

Lii O2

expressed in the form, — = — where Ci and C2 represent the

concentrations of color in two solutions and Li and L2 represent
the depths of solution traveled by the light when a color match
occurs. Applying this relation one is able to obtain the ratio of
concentrations and therefrom the concentration in one solution
if the concentration in the other be known. But as was shown
above we have, in the case of two-color indicators, different trans-
mission coefficients for various regions of the spectrum. Conse-
quently the depth of a solution cannot be altered as it is in the
ordinary colorimeter without seriously affecting the quality of the
emergent light.

When such shifts in quality occur it is impossible without the
aid of elaborate photometric devices to make an accurate com-
parison of intensities. This at once limits the usefulness of the
ordinary colorimeter, a cardinal principle of which is an accurate
device for varying and measuring the depth of view. That
feature of certain instruments whereby two optical fields are
brought into juxtaposition remains most useful.

This last and other mechanical features should at once be de-
veloped for the colorimeter devised by Gillespie (1921) which
promises to be of very great value in exact indicator work. The
principle of Gillespie's colorimeter is shown in figure 10. The
vessels A, B, C, D and E are of colorless glass the bottoms of
which should be optically polished plane-parallel. A and C are

THEORY OF INDICATORS

fixed while B may be moved up or down. The position of B is
indicated on a scale the zero mark of which corresponds to the
position of B when B and C are in contact and the 100 mark
of which corresponds to the position of B when B is in contact
with A. If now there is placed in B a solution of the acid form
of an indicator and in C a solution of the same concentration of
the indicator transformed completely to the alkaline form, it is
obvious that the position of the vessel B will determine the ratio
of the two forms of the indicator which will be within the view.

*i A

B
C

Fig. 10. Diagrammatic Section op Gillespie's Colorimeter

For comparison studies a solution to be tested is placed in E
together with that concentration of indicator that occurs in the
optical system B-C. For colored solutions tubes A and D are
used as in the Walpole system, which will presently be described.
As Gillespie has indicated this colorimeter should be useful for
certain general work where the exact principles of colorimetry
have often been neglected.

There have been two chief methods of dealing with the interfer-
ing effect of the natural color of solutions. The first method,
used by S0rensen, consists in coloring the standard comparison
solutions until their color matches that of the solution to be tested,
md subsequently adding to each the indicator.

70 THE DETERMINATION OP HYDROGEN IONS

S0rensen's coloring solutions are the following :

a. Bismarck brown (0.2 gram in 1 litre of water).

b. Helianthin II (0.1 gram in 800 cc. alcohol, 200 cc. water).

c. Tropeolin O (0.2 gram in 1 litre of water).

d. Tropeolin OO (0.2 gram in 1 litre of water).

e. Curcumein (0.2 gram in 600 cc. alcohol, 400 cc. water).
/. Methyl violet (0.02 gram in 1 litre of water) .

g. Cotton blue (0.1 gram in 1 litre of water).

The second method was introduced by Walpole (1910). It con-
sists in superimposing a tube of the colored solution over the
standard comparison solution to which the indicator is added,
and comparing this combination with the tested solution plus
indicator superimposed upon a tube of clear water.

A somewhat crude but nevertheless helpful application of Wal-
pole's principle may be made from a block of wood. Six deep
holes just large enough to hold ordinary test tubes are bored
parallel to one another in pairs. Adjacent pairs are placed as
close to one another as can be done without breaking through the
intervening walls. Perpendicular to these holes and running
through each pair are bored smaller holes through which the test
tubes may be viewed. The center pair of test tubes holds first
the solution to be tested plus the indicator and second a water
blank. At either side are placed the standards colored with the
indicator and each backed by a sample of the solution under test.
This is the so called "comparator" of Hurwitz, Meyer, and
Ostenberg (1915). Before use it is well to paint the whole block
and especially the holes a non-reflecting black. To produce a
"dead" black use a soft wood and an alcohol wood-stain. This
simple comparator is illustrated in figure 7.

One or another of the means described serves fairly well in over-
coming the confusing influence of moderate color in solutions to
be tested. In bacteriological work, however, a most serious diffi-
culty is presented by the suspension of cells and precipitates.

If one views lengthwise a tube containing suspended particles,
or even particles of grosser colloid dimensions, much of the light
incident at the bottom is absorbed or reflected before it reaches
the eye, and, if the tube is not screened, some of the light which
reaches the eye is that which has entered from the side and has
been scattered. Consequently, a comparison with a clear standard
is inadequate.

THEORY OF INDICATORS 71

S0rensen (1909) has attempted to correct for this effect by the
use of a finely divided precipitate suspended in the comparison
solution. This he accomplishes by forming a precipitate of
BaS04 through the addition of chemically equivalent quantities
of BaCl2 and Na2S04. Strictly speaking, this gives an imperfect
imitation, but like the attempt to match color it does very well
in many instances. The Walpole superposition method may be
used with turbid solutions as well as with colored, as experience
with the device of Hurwitz, Meyer and Ostenberg has shown. In
passing, attention should be called to the fact that the view of a
turbid solution should be made through a relatively thin layer.
When the comparison is made in test tubes, for instance, the view
should be from the side.

There are some solutions, however, which are so dark or turbid
that they cannot be handled with much precision by any of these
methods. On the other' hand a combination of these methods
with moderate and judicious dilution [as was indicated in Chap-
ter II this may not seriously alter the pH of a solution], permits
very good estimates with solutions which at first may appear
impossible. Some of the deepest colored solutions permit reason-
ably good determinations "and when sufficiently transparent per-
mit the application of spectrometric devices. Turbidity on the
other hand is sometimes unmanageable. Even in the case of
milk where comparison with a standard is out of the question a
two colored indicator presents a basis for judgment.

This brings us to a phase of the question the detailed analysis
of which will not be attempted. It may simply be stated as a
fact of experience that the color change of a two-color indicator,
presenting as it does change in intensities of what we may sum-
marily describe as two colors, is a change in quality which is
unmistakable within narrow limits. When there is added to this
that brilliancy which is characteristic of the sulfon phthalein
indicators the subjective aspect of indicator work is taken care
of in a way that may surprise one.

The spectrophotometer and allied instruments which have
served in many of the investigations of indicators have not yet
been brought within the range of ordinary colorimetric procedure
for the determination of pH. Where there occurs a great change
in the absorption bands, as at the endpoint of a titration, the hand

72 THE DETERMINATION OF HYDROGEN IONS

spectroscope may be applied but it is doubtful if such an instru-
ment is of much value for slight differences of virage. For the
possibilities which remain for development in this field the reader
is referred to the special literature.

This brief sketch of some of the principal aspects of indicator
theory would be incomplete were attention not called to the value
of indicators for demonstrating to students important relations
among acids and bases. Indicators also call our attention to
molecular transformations which we seldom think of as occurring
among substances the light absorptions of which are in regions of
the spectrum beyond the reach of the eye.

And finally, indicator colors bring to the thoughtful observer
their own intrinsic beauty and also reminders of how far we have
come along the road of understanding and of how very, very far
we still have to go.

CHAPTER V
Choice of Indicators

From the enormous number of colored compounds found in
nature and among the products of the laboratory many have
been called into use as acidimetric-alkalimetric indicators. Among
those of plant origin litmus and alizarine are the more familiar.
One indicator of animal origin, cochineal, an extract of an insect,
was formerly used to some extent. Walpole's (1913) treatment
of litmus, Walbum's (1913) study of the coloring matter of the
red cabbage and some of the more recent work, has given us a
little data on properties of plant and animal pigments which are
applicable to hydrogen ion determinations. But for the most
part indicators of natural origin have been neglected for the study
of synthetic compounds.

Litmus has played so important a role in acidimetry that it is
worthy of brief, special mention.

Litmus is obtained by the oxidation in the presence of ammonia
of the orcin contained in lichens, generally of the species Roccella
and Lecanora. The material which comes upon the market is
frequently in the form of cubes composed of gypsum or similar
material and comparatively little of the coloring matter. The
coloring matter is a complex from which there have been isolated
many compounds, chief among which are azolitmin, erythrolitmin,
erythrolein and spaniolitmin. Of these the azolitmin is the most
important; but the azolitmin of commerce is of uncertain compo-
sition, Scheitz (1910). The composition of the different prepara-
tions varies with the source and also with the extent of the action
of alkali and air upon the crude material.

The following method of preparing a sensitive litmus solution
is taken from Morse (1905).

The crushed commercial litmus is repeatedly extracted with fresh quan-
tities of 85 per cent alcohol for the purpose of removing a violet coloring
matter which is colored by acids but not made blue by alkalies. The resi-
due, consisting mainly of calcium carbonate, carbonates of the alkalies and
the material to be isolated, is washed with more hot alcohol upon a filter

74 THE DETERMINATION OF HYDROGEN IONS

and then digested for several hours with cold distilled water. The filtered
aqueous extract has a pure blue color and contains an excess of alkali, a
part of which is in the form of carbonate and a part in combination with
litmus. To remove the alkaline reaction the solution is heated to the boil-
ing point and cautiously treated with very dilute sulfuric acid until it be-
comes very distinctly and permanently red. Boil till all CO2 is dispelled.
Treat with a dilute solution of barium hydroxide until the color changes to
a violet. Filter, evaporate to a small volume and precipitate the litmus
with strong alcohol. Wash with alcohol and dry.

Dr. P. Rupp (private communication) prefers to make a final
washing with water which removes much of the salt at the expense
of some dye.

Synthetic indicators have for the most part displaced those of
natural origin until litmus and alizarine, turmeric and cochineal
are becoming more and more unfamiliar in the chemical labora-
tory. Indeed Bjerrum (1914) states that the two synthetic indi-
cators, methyl red and phenolphthalein, particularly because of
the zones of hydrogen ion concentration within which they change
color, are sufficient for most titrimetric purposes.

But the two indicators mentioned above cover but a very lim-
ited range of hydrogen ion concentration so that they are insuf-
ficient for the purpose we now have under consideration. A sur-
vey of indicators suitable for hydrogen ion determinations was
opened in Nernst's laboratory in 1904 by Salessky. This survey
was extended in the same year by Friedenthal, by Fels and by
Salm and the results were summarized in Salm's famous table
(cf. Z. physik. Chem., 57).

Then came the classic work of S0rensen of the Carlsberg lab-
oratory in Copenhagen. The array of available indicators had
become so large as to be burdensome. S0rensen in an extensive
investigation of the correspondence between colorimetric and
electrometric determinations of hydrogen ion concentrations re-
vealed discrepancies which were attributed mainly to the influence
of protein and salts. He chose those indicators which were rela-
tively free from the so-called protein and salt errors, constructed
solutions of known and reproducible hydrogen ion concentra-
tions and thus furnished the biochemist with selected tools of beau-
tiful simplicity. It is well to emphasize the labor of elimination
which S0rensen performed because without it we might still be
consulting such tables as that published by Thiel (1911), or the

CHOICE OF INDICATORS 75

ponderous tables 8-19, pages 84-94, and be bewildered by the
very extensive array.

S0rensen's work, coupled as it was with a most important con-
tribution to enzyme chemistry gave great impetus to the use of
indicators in biochemistry. His selection of indicators was there-
fore soon enlarged by additions of new indicators which fulfilled
the criteria of reliability which he had laid down. Alpha naphthol
phthalein, a compound first synthesized by Grabowski (1871),
was shown by S0rensen and Palitzsch (1910) to have a range
of pH 7-9 and was found useful in biological fluids. Methyl red
(Rupp and Loose, 1908) was given its very useful place by the
investigations of Palitzsch (1911). Henderson and Forbes (1910)
introduced 2-5 di nitro hydroquinone as an indicator possessing
several steps of color change and therefore useful over a wide range
of pH. Walpole (1914) called attention to several indicators of
potential value. Hottinger (1914) recommended "lacmosol,"
a constituent of lacmoid, and Scatchard and Bogert (1916)
advocated the use of dinitro benzoylene urea. There remain a
host of indicators which have been tried out in the empirical
practices of titration but which have never had their pH ranges
determined ; and there remain an unlimited number of possibilities
embodied in existing compounds such as Dox's (1915) phenol
quinolinein, Rupp's (1915) syntheses in the methyl red series
and untouched homologues of phenol phthalein and of phenol
sulfon phthalein. Furthermore, there undoubtedly are still
unsynthesized compounds of various types, old and new, which
will some day displace those now in use.

In 1915 Levy, Rowhtree and Marriott, without applying the
tests of reliability which S0rensen had employed, used phenol
sulphon phthalein in determining the pH of the dialyzate of blood.
This compound, first synthesized in Remsen's laboratory by Sohon
(1898), has received considerable attention from Acree and his
co-workers because it furnishes excellent material for the quinone-
phenolate theory of indicators. To further such studies Acree
and White had synthesized new derivatives of phenol sulphon
phthalein at the time when the work of Levy, Rowntree and
Marriott attracted the attention of Clark and Lubs. These authors
. were looking for more brilliant indicators for use in bacterial cul-
ture media and were attracted by the well known brilliance of

76 THE DETERMINATION OF HYDROGEN IONS

phenol sulphon phthalein. Through the courtesy of Professor
Acree some of the derivatives which White had prepared were
obtained. New homologues were synthesized by Lubs. The
applicability of these and numerous other indicators in the deter-
mination of the pH values of biological fluids was then studied.

In the sulfon phthalein series the following were studied:

Phenol sulfon phthalein, Sohon (1898).

Tetra nitro phenol sulfon phthalein, White and Acree (1915).

Phenol nitro sulfon phthalein, Lubs and Clark (1915).

Tetra bromo phenol sulfon phthalein, White and Acree (1915).

Tetra chloro phenol sulfon phthalein, Lubs and Clark.

Ortho cresol sulfon phthalein, Sohon (1898).

Di bromo ortho cresol sulfon phthalein, Sohon (1898).

Thymol sulfon phthalein, Lubs and Clark (1915).

Thymol nitro sulfon phthalein, Lubs and Clark.

Di bromo thymol sulfon phthalein, Lubs and Clark (1915).

a-napthol sulfon phthalein, Lubs and Clark (1915).

Carvacrol sulfon phthalein, Lubs and Clark.

Orcinol sulfon phthalein, Gilpin (1894).

The attractiveness of methyl red led to the study of the fol-
lowing compounds :

o-carboxy benzene azo mono methyl aniline, Sive and Jones
(1915).

o-carboxy benzene azo di methyl aniline, Rupp and Loose
(1908).

o-carboxy benzene azo mono ethyl aniline, Lubs and Clark
(1915).

o-carboxy benzene azo di ethyl aniline, Lubs and Clark (1915).

o-carboxy benzene azo mono propyl aniline, Lubs and Clark
(1915).

o-carboxy benzene azo di propyl aniline, Lubs and Clark (1915).

o-carboxy benzene azo (?) amyl aniline, Lubs and Clark (1915).

o-carboxy benzene azo di methyl a naphthyl amine, Howard
and Pope (1911).

o-carboxy benzene azo a naphthyl amine, Howard and Pope
(1911).

o-carboxy benzene azo di phenyl amine, Howard and Pope
(1911).

Meta carboxy benzene azo di methyl aniline, Lubs and Clark.

CHOICE OF INDICATORS 77

The mono alkyl homologues of methyl red were found to be
much less brilliant than the di alkyl compounds and were there-
fore rejected. For the same reason or because of large protein
errors we rejected the other compounds with the exception of
di ethyl and di propyl red. Of these we retained di propyl red
because it is very useful in solutions of a little lower hydrogen ion
concentration than those which may be studied with methyl red.

Propyl red is, however, not included in table 6 because it
precipitates too easily from buffer solutions to be of general
usefulness.

As the result of an extensive series of comparisons between
colorimetric and electrometric measurements, made for the most
part upon solutions of interest to bacteriologists, Clark and Lubs
(1917) suggested the series of indicators given in table 6. This
series is made up for the most part of the brilliant and more
reliable sulfon phthaleins but contains the still indispensable but
not very stable methyl red.

In the course of their investigations these authors resurrected
ortho cresol phthalein (Baeyer and Freude, 1880), found it quite
as reliable as phenolphthalein and more brilliant with a color
better adapted to titrations in artificial light.

In spite of the fact that S0rensen rejected the greater number
of the indicators which he studied and that Clark and Lubs, after
a resurvey of the subject and the preparation of many new com-
pounds, listed but few indicators as reliable, there has recently
appeared a tendency to resurrect the rejects. Now many of
these are useful in special cases and undoubtedly there is an
occasional individual to be found in the lists which has been
insufficiently studied and unjustly rejected. Nevertheless, the
indiscriminate use of miscellaneous indicators may lead to gross
errors or at least to such a diversity of data that their correlation
will become complex during the coming period when the Specific
salt-errors and general conduct of the individual indicators are
still being worked up.

It is therefore advisable to use the more thoroughly studied
lists. Three such lists are given (tables 5, 6 and 7). The indi-
cators therein listed should cover all ordinary needs. S0rensen's
list is given in table 5 and to this is appended S0rensen's
comments. For general purposes the selection of indicators given

THE DETERMINATION OF HYDROGEN IONS

in table 6 will be found the most satisfactory especially because
of their brilliancy. Each of these however has its own special
limitations as every indicator has. For the study of colorless
solutions where salt errors are to be reduced the nitro phenols
listed in table 7 should be valuable.

TABLE 5

Sfirenseri's selected indicators

Figures in parentheses refer to Schultz (1914). Figures 1-20 are S0rensen's

INDICATOR

10.
11.

12.
18.

14.
15.
16.
17.

18.
10.

20.

Methyl violet 6B extra, (517)

Mauvein, Rosolane, (688)

Diphenylamino-azo-benzene

Diphenylamino-azo-p-benzene sulfonic acid, Tro-
paeolin 00, (139)

Diphenylamino-azo-m-benzene sulfonic acid, Metanil
yellow, (134)

Benzyl anilino-azo-benzene

Benzylanilino-azo-p-benzene sulfonic acid

Metachloro diethyl-anilino-azo-p-benzene sulfonic
acid

Dimethyl anilino-azo-benzene, (32)

Methyl orange, Helianthine, (138)

a naphthylamino-azo-benzene

a-naphthylamino-azo-p-benzene sulfonic acid

Para nitro phenol

Neutral red, (670)

Rosolic acid, Aurin, (555)

Orange I, Tropaeolin 000 No. 1, (144)

Phenolphthalein.

Thymolphthalein

Paranitrobenzene-azo-salicylic acid, Alizarine yel-
low R, (58)

Resorcin-azo-p-benzene sulfonic acid, Tropaeolin 0,
(143)

pH RANGE

0.1-

3.2

0.1-

2.9

1.2-

2.1

1.4-

2.6

1.2-

2.3

2.3-

3.3

1.9- 3.3

2.6-

4.0

2.9- 4.0

3.1-

4.4

3.7-

5.0

3.5-

5.7

5.0- 7.0

6.8-

8.0

6.8-

8.0

7.6- 8.9

8.3-

10.0

9.3-

10.5

10.1-

12.1

11.1-

12.7

In tables 8-20 are a few indicators which are undoubtedly
reliable but little used, a few which are definitely unreliable
though often used, and very many of uncertain character but
for the most part bearing the stamp of disapproval by competent
judges. Since the indicators in tables 5, 6 and 7 cover all ordinary
requirements it seems hardly worth while to venture upon an
analysis of the remaining tables.

CHOICE OF INDICATORS 79

In table 5 is S^rensen's list of indicators; concerning these indicators
S0rensen remarks:

Not all these indicators furnish equally well defined virages and above
all they are not of equal applicability under all circumstances. In the
choice of an indicator from among those which we have been led to recom-
mend it is necessary to use judicious care and especially to take into con-
sideration the following facts:

a. The indicators of the methyl violet group (nos. 1 and 2) (see table 5)
are especially sensitive to the action of neutral salts; furthermore the in-
tensity of color changes on standing and the change is the more rapid the
more acid the medium.

b. The basic indicators (nos. 3, 6, 9, 11, 14) are soluble in toluene and in
chloroform. The first four separate partially on prolonged standing of
the experimental solution.

c. In the presence of high percentages of natural proteins most of the in-
dicators are useless although certain of them are still serviceable; nos. 1, 2,
13, 16, 17, 18.

d. In the presence of protein decomposition products even in consid-
erable proportions the entire series of indicators may render real service.
Yet even in these conditions some of the acid azo indicators may give
notable errors (nos. 4, 5, 7, 8, 10) in which case one should resort to the cor-
responding basic indicators.

e. When only small percentages of protein or their decomposition prod-
ucts are concerned the acid azo indicators are more often preferable to
the basic for they are not influenced by toluene or chloroform and do not
separate from solution on standing.

/. In all doubtful cases — for example in. the colorimetric measurement
of solutions whose manner of reaction with the indicator is not known, the
electrometric measurement as a standard method should be used. Then
the worth of the indicator will be determined by electrometric measurement
with colorimetric comparison.

In table 6 will be found the final selection of Clark and Lubs
with the common names which they suggested for laboratory par-
lance, the concentration of indicator convenient for use, a rough
indication of the nature of the color, and the useful pH range.

With the improved method for the preparation of the sulfon
phthalein indicators described by Lubs and Clark (1915) they may
easily be made from materials readily obtained. The indicators
can also now be purchased in this country and abroad from
chemical supply houses.

The indicators recommended by Clark and Lubs are marketed
both in the form of a dry powder and in stock solutions. In cases
where the acidity of the free acid dye in the indicator solution

THE DETERMINATION OF HYDROGEN IONS

does not interfere with accuracy and when alcohol is not objec-
tionable the alcoholic solutions of the dyes may be used. Clark
and Lubs prefer to use aqueous solutions of the alkali salts in
concentrations which may be conveniently kept as stock solu-
tions. These are diluted for the test solutions used in the drop-
ping bottles.

TABLE 6
Clark and Lubs' list of indicators

CHEMICAL NAME

COMMON NAME

S5
I 0

B <
o

COLOR CHANGE

RANGE

Thymol sulfon
phthalein (acid
range)

Thymol blue (see
below)

Brom phenol blue

Methyl red

Brom cresol pur-
ple

Brom thymol blue

Phenol red

Cresol red

Thymol blue

Cresol phthalein

per cent

0.04

0.02

0.04

0.04
0.02
0.02
0.04
0.02

Red-yellow

Yellow-blue

Red-yellow

Yellow-purple

Yellow-blue

Yellow-red

Yellow-blue

Colorless-red

1.2-2.8

Tetra bromo phenol
sulfon phthalein

Ortho carboxy ben-
zene azo di methyl
aniline

3.0-4.6
4.4-6.0

Di bromo ortho cre-
sol sulfon phthal-
ein

5.2-6.8

Di bromo thymol
sulfon phthalein

Phenol sulfon phthal-
ein

6.0-7.6
6.8-8.4

Ortho cresol sulfon
phthalein

7.2-8.8

Thymol sulfon
phthalein

8.0-9.6

Ortho cresol phthal-
ein

8.2-9*8

For the preparation of these stock solutions one decigram (0.1
gram) of the dry powder is ground in an agate mortar with the
following quantities of N/20 NaOH. When solution is complete
dilute to 25 cc. with water.

CHOICE OF INDICATORS

MOLECULAR WEIGHT

INDICATOR

N/20 NaOH per

DECIGRAM

354
669
382
540
466
624
269

Phenol red
Brom phenol blue
Cresol red
Brom cresol purple
Thymol blue
Brom thymol blue
Methyl red

CC.

5.7
3.0
5.3
3.7
4.3
3.2
7.4

If there be no particular reason to maintain exact equivalents
it may be found easier to dissolve the dyes in 1.1 equivalents of
alkali instead of one -equivalent as indicated above.

When made up to 25 cc. as noted above there is obtained in
each case a 0.4 per cent solution of the original dye itself. For
tests they should be diluted further. To place the dyes upon a
comparable basis the final dilution should be nearly the same when
calculated upon a molar basis and, by reason of the great change in
molecular weight caused by the introduction of bromine and other
group substituents, equal molecular concentrations will be very
far apart in percentage concentration. For all ordinary pur-
poses, however, this may be neglected and the solutions mentioned
above if diluted in each case to a concentration of 0.04 per
cent will be found satisfactory for use in testing 10 cc. of a solu-
tion with about five drops of indicator.

From various sources have come complaints that the method
outlined above for the preparation of the aqueous alkali salt
solution of brom cresol purple leads to a solution of much lower
tinctorial power than when the same material is taken up directly
in alcohol. No such difficulty was experienced with the material
described by Lubs and Clark but it has appeared not infrequently
since. The source of the difficulty is not yet definitely traced,
but is suspected to be due to impurities. If so it should be
avoided by purchasing the highly purified material which is now
made specially.

While the aqueous alkali salt solution of methyl red is preferred
for some purposes a methyl red solution can be more conveniently
prepared by dissolving 1 decigram in 100 cc. alcohol and diluting
to 200 with distilled water.

82 THE DETERMINATION OF HYDROGEN IONS

Ortho cresol phthalein and phenol phthalein are used in a
0.04 per cent solution of 95 per cent alcohol.

Methyl red and brom cresol purple may be recrystallized from
hot toluol, cresol red and brom phenol blue from glacial acetic
acid, thymol blue from hot alcohol.

Tables 8-20 have been compiled with the aid of Dr. Barnett
Cohen and Dr. Elias Elvove with several purposes in view. In
the first place there exist in the older literature a great many
observations recorded in terms of the color of a given indicator.
These data can often be translated into modern terms if the pH
range of the given indicator is known. In the second place there

TABLE 7

Michaelis' indicators and their ranges as used in the method of Michaelis and

Gyemant (see Chapter VIII)

Picric acid colorless 0.0- 1.3 yellow

2, 4-dinitro phenol colorless 2.0- 4.7 yellow

a dinitro phenol

2, 6-dinitro phenol colorless 1.7- 4.4 yellow

/3 dinitro phenol

2, 5-dinitro phenol colorless 4.0- 6.0 yellow

y-dinitro phenol

m-nitro phenol colorless 6.3- 9.0 yellow

p-nitro phenol colorless 4.7- 7.9 yellow

Phenolphthalein colorless 8.5-10.5 red

Alizarine yellow GG colorless 10.0-12.0 yellow

Salicyl yellow

are circumstances when for one reason or another it becomes
necessary to draw upon the miscellaneous list. It should there-
fore be available. Lastly, and perhaps most important, our review
of the literature and of indicator labeling has shown that there
is great confusion and an initial step in the clarification of the
subject will be taken if there is available a tabulation of existing
data to serve as a basis for revision.

In examining a large collection of indicators the labeling
was found to be insufficient in a large percentage of cases. On
studying the literature we find evidence that others have
encountered the same difficulty without stating so, for in
many instances the indicator names given were evidently those

CHOICE OF INDICATORS 83

of one or another dealer who cared so little for the scientific uses
of his commodity that he left from the label the designation
essential to its identification. This habit has become more or less
prevalent. In some instances our own uncertainty may be due
to an arbitrary adherence to the nomenclature found in various
editions of Schultz. For instance when we see the indicator
crocei'ne listed and refer to Schultz (1914) we find four crocei'nes
with various distinguishing marks and seven other compounds
for the names of which "croceme" is used in one or another com-
bination. But Schultz lists no croceme. We are not helped in going
back to the lists of Schultz and Julius (1902). Now we might
assume that "croceme" was used in Salm's table as a term having
a definite meaning outside the dye industry. On this principle
we should find that "helianthine" has been employed in accordance
with scientific usage. However we find that an old sample of
helianthine from Salm's dealer is not the helianthine of methyl
orange but corresponds in pH-range to Salm's Helianthine I,
which, together with Salm's Helianthine II we have not identified.

Again there are other difficulties such as are illustrated by the
case of Tropaeolin OOO No. 1 and Tropaeolin 000 No. 2. No. 1
is prepared from p-sulfanilic acid and a-naphthol. No 2 is pre-
pared from p-sulfanilic acid and (3-naphthol. In this there is
agreement by Schultz and Julius 1902, Green 1904 and Beilstein
(third edition). In accord with this S0rensen describes his
a-naphthol preparation as Tropaeolin 000 No. 1. In the second
edition of Indicators and Test Papers, Cohn (1914) has given
synonyms for the a and /3 compounds which agree with Green,
but has reversed the No. 1 and No. 2 at the headings of his de-
scriptions and uses "No. 1" and "No. 2" inconsistently in the
text. Prideaux (1917) has called the /3 compound Tropaeolin
000 and gives the range as 7.6-8.9, which looks suspiciously like
S0rensen's 7.6-8.9 for the a compound. Prideaux uses the
synonym. Orange II for the /3 compound in .harmony with Green
but on the next page describes the a compound as Orange II.
The identity of Salm's Tropaeolin 000 is not clear. It was
evidently different from the Tropaeolin 000 No. 1 used by
S0rensen. We find that an old sample with the label "Tro-
paeolin 000" agrees with neither S0rensen's nor Salm's data.

Many other instances might be cited to show the confused

THE DETERMINATION OF HYDROGEN IONS

state of the subject. Because it is serious the reader will have
to use the following tables with caution, and he need not be
surprised if a sample of indicator which he tests does not give
a pH range corresponding to that recorded.

In the compilation of the lists we have followed competent
advice in using the nomenclature of Farbstofftabellen, Gustav

TABLE 8
Nitro compounds

SERIAL
NUM-
BER

INDICATOR

pH RANGE

Picric acid (5)

colorless

colorless
light yellow

colorless

pink

colorless
colorless
colorless
colorless

colorless
pink

0.0- 1.3 yellow

1.7- 4.4 yellow
2.0- 4.0 yellow

2.0- 4.7 yellow
3.0- 9.0 various
colors
3.9- 5.9 yellow

4.0- 6.0 yellow

4.1— 5.6 yellow

2
3

2, 4, 6-trinitro-phenol

2, 6-Dinitro-phenol (fi)

Martius yellow (6)

4
5

7
8

2, 4-dinitro-a-naphthol

2, 4-Dinitro-phenol (a)

2, 5-Dinitro-hydroquinone

2, 3-Dinitro-phenol (e)

2, 5-Dinitro-phenol (7)

iso-Picramic acid

9
10

2, 6-dinitro-4-amino-
phenol

3, 4-Dinitro-phenol (5)

p-Nitro-phenol

4.3- 6.3 yellow
5.0- 7.0 yellow

11
12

Dinitrobenzoylene-urea .. . .

m-Nitro-phenol

6.0- 8.0 yellow
6.3- 9.0 yellow

Nitramine (?)

11.0-12.5

14
15

1, 3, 5-Trinitro-benzene

2, 4, 6-Trinitro-toluene (TNT)

11.5-14.0 orange
11.5-14.0 orange

Schultz, fifth revised edition, Berlin, 1914. In a few cases there
have been added to the synonyms in table 20 terms which are
obsolete in the dye industry but which are still used in the nomen-
clature of indicators. Schultz numbers are to be found in tables 8
to 19 following the name of each indicator when the given indi-
cator is listed by Schultz. Since it is unimportant for indicator
work, no distinction has been made between acids and their salts.
The classification by structure follows in the main that of Schultz.

CHOICE OF INDICATORS

TABLE 9
Monoazo compounds

SERIAL

NUM-

INDICATOR

pH RANGE

,BER

Curcumein (?)

orange

0.0- 1.0 yellow,

yellow 13-

15 green

o-Carboxybenzene-azo-(di or

mono?) amyl-aniline . . .

purple

0.0- 1.6 orange (fluo-
rescent),
orange 5.6-
7.6 yellow

o-Carboxybenzene-azo-m-

yellow

0.0- 4.6 orange,

orange 4.6-
7.6 yellow

p-Toluene-az o-pheny 1-aniline .

1.0- 2.0

p-Carboxybenzene-azo-di-
methyl-aniline (Para

methyl red)

red

1.0- 3.0 yellow

p-Toluene-azo-pbenyl-a-naph-

thylamine

1.1- 1.9

Benzene-azo-diphenylamine. .

1.2- 2.1

Metanil yellow extra (134)....
m-sulfobenzene-azo-di-
phenylamine

red

1.2-2.3 yellow

Benzene-az o-pheny 1-a-n aph-

thylamine

1.4- 2.6

Orange IV (139)

pink

1.4- 2.6 yellow

p-sulfobenzene-azo-di-

phenylamine

o-Toluene-azo-o-toluidine. . . .

1.4- 2.9

p-Toluene-azo-benzyl-a-

naphthylamine

1.6- 2.6

• 28

p-Toluene-azo-benzyl-aniline.

1.6- 2.8

Benzene-azo-benzyl-a-naph-

1.9- 2.9

light yellow

1.9- 3.3 yellow

p-Benzenesulfonic acid-azo-

aniline

1.9- 3.3

p-Benzenesulfonic acid-azo-

benzyl-aniline

1.9- 3.3

m-Carboxybenzene-azo-di-

methylaniline

red

2.0- 4.0 yellow
2.3- 3.3

Benzene-azo-benzyl-aniline.. .

THE DETERMINATION
TABLE 9-

OF HYDROGEN IONS

Continued

SERIAL

NUM-

INDICATOR

pH RANGE

BER

p-Benzenesulfonic acid-azo-
metachloro-dimethyl-

aniline

2.6- 4.0

Orange III (47)

red

2.6- 4.6 yellow

m-nitrobenzene-azo-/3-

naphthol-3, 6-disulfo-

nic acid

Butter yellow 0 (32)

red

2.9- 4.0 yellow

benzene-azo-dimethyl-

aniline

o-Carboxybenzene-azo-di-

phenylamine

pink

3.0- 4.6 yellow,

purple 0.0-

1.6 pink

p-Benzenesulfonic acid-azo-

methyl-aniline

3.1- 4.2

p-Benzenesulfonic acid-azo-

ethyl-aniline

3.1- 4.4

Methyl orange (138)

orange red

3.1- 4.4 yellow

p-benzenesulfonic acid-

az o-dimethy 1-aniline

p-Benzenesulfonic acid-azo-
diethyl-aniline (Ethyl

orange)

pink

3.5- 4.5 yellow

p-Benzenesulfonic acid-azo-

a-naphthylamine

3.5- 5.7

Benzene-azo-a-naphthyl-

amine

3.7- 5.0

p-Toluene-azo-a-naph-

thylamine

3.7- 5.0

o-Carboxybenzene-azo-mono-

methylaniline

red

4.0- 6.0 yellow

Chrysoidin (33)

orange

4.0- 7.0 yellow

benzene-azo-m-phenyl-

enediamine

o-Carboxybenzene-azo-mono-

ethylaniline

red

4.2- 6.2 yellow

o-Carboxybenzene-azo-mono-

n-propylaniline

red

4.2- 6.2 yellow

o-Carboxybenzene-azo-di-

methylaniline (Methyl

red)

red

4.2- 6.3 yellow

o-Carboxybenzene-azo-di-

ethvlaniline

red

4.4- 6.2 yellow

' J v

CHOICE OF INDICATORS
TABLE 9— Concluded

1ERIAL

NUM-

INDICATOR

pH RANGE

BER

o-Carboxybenzene-azo-di-n-
propylaniline (Propyl

red)

red 4.6- 6.6 yellow

Benzene-azo-dimethyl-a-

naphthylamine

4.8- 5.5

p-Benzenesulfonic acid-azo-
dimethyl-a-naph-

thylamine

5.0- 5.7

o-Carboxybenzene-azo-a-

naphthylamine

pink 5.6- 7.0 yellow

o-Carboxybenzene-azo-di-
methyl-a-naphthyl-

amine

red 5.6- 7.6 orange

Naphthylamine brown (160) . .
4-sulf onaphthalene-az o-
a-naphthol

orange 6.0- 8.4 pink

6-Sulf o-a-naphthol-1-az o-m-

hydroxybenzoic acid . . .

orange 7.0- 8.0 blue,

violet 12-
13 red

Orange I (144)

7.6- 8.9

p-sulfobenzene-azo-a-

naphthol

Orange II (145)

7.6- 8.9 (?)

p-sulfobenzene-azo-/S-

naphthol

Alizarine yellow GG (48)
m-nitrobenzene-azo-sali-
cylic acid

colorless 10.0-12.0 yellow

Alizarine yellow R (58)

p-nitrobenzene-azo-sali-
cylic acid

pale yellow 10.1-12.1 orange .

Fast red A (161)

10.5-12.1

5-sulfonaphthalene-azo-

/3-naphthol

Fast red B (112)

pink 10.5-12.5 orange

a-naphthalene-azo-/8-

naphthol-3, 6-disulfo-

nic acid

Chrysoin (143)

p-sulfobenzene-azo-
resorcin

yellow 11.1-12.7 orange

Orange G (38)

yellow 11.5-14.0 pink

benzene-azo-/8-naphthol-

7-disulfonic acid

THE DETERMINATION OF HYDROGEN IONS

TABLE 10
Disazo compounds

SERIAL

NUM-

INDICATOR

pH RANGE

BER

Benzopurpurin B (365)

blue-0.3- 1.0 violet,

ditolyl-disazo-bi-/3-naph-

violet 1.0-

thylamine-/3-sulfonic

5.0 yellow,

acid

yellow 12.0-
14.0 rose

Congo (307)

blue 3.0- 5.0 red

diphenyl-disazo-binaph-

thionic acid

Azo blue (377)

violet 10.5-11.5 pink

ditoly 1-disaz o-bi-a-n aph-

thol-4-sulfonic acid

TABLE 11
Triphenylmethane compounds

SERIAL

NUM-

INDICATOR

pH RANGE

BER

Crystal violet (516)

green

0.0- 2.0 blue

hexamethyl pararo-

saniline

Malachite green (495)

yellow

0.0- 2.0 green,

tetramethyl-di-p-amino-

blue 11.5-

triphenyl-carbinol

14.0 fades

Red violet 5R extra (514)

mixture of mono-, di- and
tri-methyl or ethyl ro-
sanilines and pararo-
sanilines

green

0.0- 2.0 blue

Brilliant green (499)

yellow

0.0- 2.6 green

tetraethyl-di-p-amino-

triphenyl-carbinol

Iodine green

yellow

0.0- 2.6 blue

heptamethyl rosaniline

Ethyl violet (518)

yellow

0.0- 3.6 blue

hexaethyl pararosaniline

Ethyl green (methyl green)...
ethyl-hexamethyl-para-
rosaniline bromid

0.1- 2.3

CHOICE OF INDICATORS 89

TABLE 11-

■Continued

tERIAL
NUM-
BER

78
79
80

81
82

INDICATOR

pH RANGE

Methyl violet 6B extra (517)..
mixture of benzyl-tetra-
and pentamethyl-p-
rosaniline and hexa-
methyl-p-rosaniline

Fuchsin (512) (base)

0.1- 3.2

purple 1.2- 3.0 fades
pink 3.6- 6.0 colorless

mixture of rosaniline and
pararosaniline
Red violet 5ES (525)

trisulfonate of ethyl ro-
saniline
Water blue (539)

blue 4.7- 7.0 colorless,*

di- and tri-sulfonic acids

of triphenyl-p-rosani-

line and di-phenyl-ro-

saniline

Aurin (p-rosolic acid) (555)...

complex mixture
Alkali blue (536)

purple 10.5-
14.0 rose

yellow 6.9- 8.0 red
lilac 9.4-14.0 pink

mixture of diphenyl-ro-
saniline-mono-sulfonic
acid and triphenyl-
pararosaniline-mono-
sulfonic acid
Methyl blue (538)

blue 10.0-13.0 pink

triphenylpararosaniline-
di- and trisulf onic acids
Fuchsin S (524)

red 12.0-14.0 fades

di- and trisulfonic acids
of rosaniline and p-ro-
saniline

* Samples of Water blue (China blue) which we have tested vary con-
si lerably. The color change in the neutral range is instantaneous with
s< me samples but requires a long period (several hours at room tempera-
t\ re) for others.

TABLE 12
Quinoline compounds

81 RIAL
1 OTH-
ER

INDICATOR

pH RANGE

Quinoline blue (Cyanin) (611).
C28H35N2I

colorless 7.0-8.0 violet

TABLE 18
Oxazine compounds

SERIAL

NUM-

INDICATOR

pH RANGE

BER

Alizarin green B (657)

lilac-0.3- 1.0 flesh,

dihydroxy-naphth-azox-

brownish yel-

onium sulfonate

low 12.0-
14.0 brown,
then green

Nile blue 2B (654)

blue 7.2- 8.6 rose

diethyl-benzyl-diamino-

naphtho-phenazoxon-

ium chlorid

Nile blue A (653)

blue 10.2-13.0 rose

diethyl-diamino-naphtho-

phenazoxonium sulfate

TABLE 14

Azines

SERIAL

NUM-

INDICATOR

pH RANGE

BER

Methylene violet BN powder

(680)

purple

0.0- 1.2 violet

dimethyl-diamino-

phenyl-phenaz onium

chloride

Rosolane (688)

0.1- 2.9

phenyl and tolyl

safranines

Rose magdala (694)

rose

3.0- 4.0 red,

mixtures of amino naph-

lilac 12.0-

thyl-naphthazonium

14.0 violet

chlorid and diamino-

n aphthy 1-n aphthaz on-

ium chloride

Indulin, spirit soluble (697) . .
mixtures of dianilido-
amido-tri-anilido- and
tetranilido-phenyl-
phenazonium chlorides

blue

5.6- 7.0 violet

Neutral red (670)

red

6.8- 8.0 yellow

dimethyl-diamino-tolu-

phenazine

Neutral blue (676)

9.3-10.2

dimethyl-amino-phenyl-

phenonaphthazonium

chloride

CHOICE OF INDICATORS

TABLE 15
Anthraquinone compounds

iERIAL

NUM-

INDICATOR

pH RANGI

BER

Alizarin Blue X (803)

dihydroxy-anthra-
quinone-/S-quinoline

pink

0.0-1.6

yellow,
yellow 6.0-
7.6 green

Purpurin (783)

yellow

0.0-4.0

orange,

1, 2, 4-trihydroxy-anthra-

orange 4.0-

qumone

8.0 rose,
lilac 12.0-
14.0 violet

Alizarin red S (780)

yellow

5.0-6.8

pink

mono sulfonic acid of

alizarin Vi

Alizarin Vi (Alizarine) (778)...
1, 2-dihydroxy-anthra-
quinone

yellow

5.5-6.8

red,

violet 10.1-
12.1 purple

Alizarin Blue S (804)

yellow

6.0-8.0

green,

Na bisulfite compound of

green 11.0-

alizarin blue X

13.0 blue

TABLE 16
Indigos

E 3RIAL
DUM-
BER

.00

INDICATOR

Indigotine la in powder (In-
digo carmine) (877) . . .
Indigo disulfonate

pH RANGE

blue 11.6-14.0 yellow

THE DETERMINATION OF HYDROGEN IONS

TABLE 17
Phthalein and xanthone compounds

SERIAL

NUM-
BER

INDICATOR

pH RANGE

101

Rhodamine B (573)

orange -
yellow

orange

pink

light yellow

yellow

yellowish
yellowish
colorless
colorless
colorless
colorless
colorless
pink

-0.1- 1.2 pink
0.0- 2.6 brown,

102

diethyl m-amino-phenol-
phthalein
Gallein (599)

103

pyrogallol phthalein
E©sin G (587)

brown 3.6-
7.0 pink,

pink 9.4-
14.0 purple
0.0- 3.0 pink

0.0- 3.6 pink

1.4- 3.6 red

3.6- 5.6 yellow (fluo-
rescent)

4.0- 6.6 yellow (fluo-
rescent)

7.0- 9.0 green

7.0- 9.0 blue

8.0- 9.0 violet

8.2- 9.8 red

104

tetrabromo fluorescein
Erythrosin*

105
106

107

Phloxin Red BH (Griibler). . .
Uranin (Fluorescein) (585) . . .

resorcin phthalein
Dichloro fluorescein

108
109
110
111

o-a-Naphthol phthalein

p-a-Naphthol phthalein

Tetrabromophenol phthalein.
o-Cresol phthalein

112

Phenol phthalein

8.3-10.0 red

113

114

1, 2, 3-Xylenol phthalein

Thymol phthalein

8.9-10.2 blue
9.3-10.5 blue

115

Eosin BN (590)

10.5-14.0 yellow

dibromo dinitro fluo-
rescein

* The identity of this erythrosin is in doubt. Erythrosin R, G, yellow-
ish, and Iodeosin G are synonyms of di-iodo-fluorescein. Erythrosin extra
bluish, D, B, J extra, JNV, W extra, and Iodeosin B are synonyms for the
tetra-iodo-fluorescein .

CHOICE OF INDICATORS

TABLE 18
Sulfonphthaleins

SERIAL

NUM-

INDICATOR

pH RANGE

BER

116

Di-iodophenol sulfon-

phthalein*

orange

0.0- 1.2 yellow,

yellow 3.2-

7.0 purple

117

pink

0.2- 0.8 orange,

yellow 4.0-

7.0 green,
violet 8.5-

10.2 blue,
blue 10.2-

12.5 green

118

Thymol sulf onphthalein
Thymol blue

(acid range)

red

1.2- 2.8 yellowf,

(alkaline range)

yellow 8.0-

119

Tetranitrophenol sulfon-

9.6 blue

phthalein

yellow

2.8- 3.8 red

120

Tetrabromophenol sulfon-

phthalein

yellow

3.0- 4.6 blue

Brom phenol blue

121

Tetrachlorophenol sulf on-

phthalein

• yellow

3.0- 4.6 blue

122

Dibromo-o-cresol sulfon-

phthalein

yellow

5.2- 6.8 purple

Brom cresol purple

.23

Dibromothymol sulfon-

phthalein

yellow

6.0- 7.6 blue

Brom thymol blue

Phenol nitro sulf onphthalein.

yellow

6.6- 8.4 purple

Phenol sulf onphthalein

Phenol Red

yellow

6.8- 8.4 red

o-Cresol sulfonphthalein

Cresol Red

yellow

7.2- 8.8 red

Salicyl sulfonphthalein

yellow

7.2- 9.2 pink

Thymol nitro sulfonphthalein.

yellow

7.2- 9.4 blue

a-Naphthol sulfonphthalein . .

yellow

7.5- 9.0 blue

Carvacrol sulfonphthalein

yellow

7.8- 9.6 blue

Orcin sulfonphthalein

yellow

8.6-10.0 pink (fluo-
rescent)

Nitrothymol sulfonphthalein.

violet

9.2-11.5 yellow

* Purity not established.

f All sulfonphthaleins show color changes at high acidities but those
o thymol sulfonphthalein are the most useful.

TABLE 19
Miscellaneous indicators

SERIAL

NUM-

INDICATOR

pH RANGE

BER

133

Croceine (?)

■ blue-

-0.3- 0.0 rose,

rose 12.0-

14.0 violet

134

green

-0.3- 1.0 blue,

violet 14.0-
15.0 lilac

135

Safranin (679?)

blue-

-0.3- 1.0 red,

red 14.0-
15.0 violet

136

Hematein (Logwood) (938) . . .

variable

from

0.0-15.0

137

Gentian violet

0.4- 2.7

138'

Red cabbage extract

red

2.4- 4.5 green

139

1-Oxy-naphtho-chino-

methane

colorless

2.7- 3.7 purple

2.8- 4.0 yellow

140

Troger and Hille's indicator. .

orange

C14H16N4SOsH

141

Phenacetolin

yellow

3.0- 6.0 red,

red 10.0-

13.0 colorless

142

Lacmosol

red
red
red

4.4— 5.5 blue

143

Lacmoid

4.4- 6.2 blue

144

Azolitmin (Litmus)

4.5- 8.3 blue

145

Carminic acid (from cochi-

neal) (932) '.

orange

4.6- 7.8 rose,

violet 11.0-

14.0 pink

146

Cochineal (932)

yellow
pink

4.8- 6.2 lilac

147

Archil (Orchil) (934)

5.6- 7.6 lilac

148

Brazil wood, Redwood, Bra-

silein (935)

colorless

6.0- 8.0 pink
7.0- 8.0 greenish
7.3- 8.7 green

149

Guaiac tincture

colorless

150

Lygosine

yellow

di-o-hydroxy-styryl

ketone

151

Mimosa flower extract

7.7- 9.6

152

Turmeric (Curcuma) (927) . . .
C21H20O6

yellow

8.0-10.2 orange

153

Alkanin

red
yellow
purple
orange

8.3-10.0 blue

154

a-Naphthol benzein

8.5- 9.8 green

155

Benzoazurin (?)

10.5-12.0 pink
11.0-12.0 orange red

156

Helianthin I (?)

157

Poirrier's blue

blue
brownish-
yellow

11.0-13 0 red

158

Helianthin II (?)

13.0-14.0 lilac

CHOICE OF INDICATORS

TABLE 20
The more common synonyms of indicators

This table contains the names and synonyms of the various indicators
in alphabetical order. Following each name, or group of synonyms, is a
number in bold face type. This number is the serial number of the com-
pound as found in the preceding tables.

Some names apply to two or more entirely different dyes. If such dyes
are in our tables, their serial numbers are given; and if the particular dyes
are not in the preceding tables there is given in italics in parentheses the
1914 Schultz number and name. Thus: "Helianthin, 36, 41 (141, Azogelb
SG cone.)," means that the name Helianthin is applied to Orange III, to
Methyl orange and to Schultz No. 141, Azogelb 3G cone.

Acetin blue R 92

Acid fuchsin, B, G, O, S 84

Acid magenta, 0 84

Acid orange 60

Acid yellow, cryst, D extra, DMP 25

Acid yellow RS 65

Acme yellow 65

Alizarin, le 98

Alizarin-Blaustich I and la 98

Alizarin blue A, ABI, BM in Teig, C,
DNW in Teig, F, G, GG, GW, R,
RR, RR in Teig, WA in Teig, WC,
WN in Teig, WR, WRR, WX, X, XA

in Teig 95

Alizarin blue S, SR, SRW, SW 99

Alizarin blue soluble ABS 99

Alizarin carmine 97

Alizarin dark blue S, SW 99

Alizarin green B 86

Alizarin mono sulfonate 97

Alizarin No. 1 98

Uizarin No. 6 96

Uizarin orange R, 2R-paste and powder.. 62

Uizarin P 98

Uizarin powder SA, W, W extra 97

dizarin purpurin 96

dizarin red IWS, S 97

. dizarin sulfacid 97

. dizarin yellow G, GG, GGW, 3G paste

and powder 61

. dizarin yellow R, RW paste and powder 62

. lizarin VI 98

. lizarin violet 102

L lkah" blue, B-5B, No. 2, No. 4, No. 6,

R-5R, RR 82

i lkanin , 153

i midoazobenzol 30

i nilin brown 78

i nilin purple 90

i nilin red 78

i nilin yellow 3, 30

i nthracene yellow GG 61

Anthracene yellow RN 62

Anthracene violet 102

Anthraquinone compounds Table 15

Archelline 2B ." . . . 64

Archil 147

Atlas orange 60

Aurin 81

Azalein 78

Azin blue spirit soluble 92

Azines Table 14

Azo blue 69

Azo-bordeaux 64

Azolitmin 144

Azo compounds Table 9

Baumwollrot 4B 68

(.363, Benzopurpurin 4B)

Baumwollrot B 67, 68

Baumwollrot C 68

Beizengelb2 GT 61

Beizengelb 3R, PN 62

Benzal green 00 71

Benzoazurin 155

Benzoin blue R 69

Benzopurpurin B 67

Benzyl violet, 7B 77

Betanaphthol orange 60

Bitter almond oil green 71

Blau CB, spirit sol 92

Bleu alcalin, 4B 82

Bleu 3BS, C4B, de Lyon 0 80

Bleu methyl 83

Bleu neutre 94

Bleu Nicholson 4B ' 82

Bleu soluble pur 80

Blue extra, water soluble for wool and

silk 80

Bogert and Scatchard's indicator 11

Bordeaux B, BL, R, R extra 64

Bordeaux G 64

(254, Bordeaux G)

Brasilein; brasilin 148

Braun salz R 47

THE DETERMINATION OF HYDROGEN IONS

TABLE 20- Continued

Brazil wood 148

Brilliant f uchsin 78

Brilliant green, crystals, cryst. No. 1, 3,

4, extra, II, O, S, Y 73

Brilliant violet 6B, 8B 77

Brom cresol purple 122

Brom eosin 103

Brom phenol blue 120

Brom thymol blue 123

Butter yellow 0 37

Campeche wood 136

Cardinal, R, G 78

Cardinal red 63

Cardinal red B, G, R 78

Carmine, lake 146

Carminic acid 145

Cerasin 63

Cerasine, R ' 64

China blue 80

China green cryst 71

Chrombrown RO 57

Chrysoidin 47

(84, Chrysoidin R)
Chrysoidin A cryst., -Fettfarbe, G, 2G

extra, J, JEE, RE, Y, Y extra 47

Chrysoidin R 47

(34 also 69, Chrysoidin R)

Chrysoin, G 65

Citronine V double 25

Cochineal 146

Congo; Congo red; Congo red R 68

Corallin 81

Cotton blue 80, 83

Cotton blue 3B, cone. No. 1, No. 2, cone.

R, extra 80

Cotton red B 67, 68

Cotton red, cone 68

Cresol red 126

Croceine 133

Crystal violet, extra cryst. 5B, 5BO, 6B,

N powder, O, P cryst 70

Cudbear 147

Curcuma 152

Curcumein* 16

Curcumin 152

Cyanin 85

Dahlia 72

Dechan's indicator 102

Degener's indicator 141

Diamant f uchsin 78

Diamant griin 71

Diamant grttn B 71

(276, Diamantgrun B)

Diamant grttn G 73

Dianilrot R 68

Disazo compounds Table 10

Dianthine B 104

Dichlorofluorescein 107

Dimethylaniline orange 41

Diphenylamin blue 83

Direct red C 68

Ecarlate J, JJ, V 115

Echtblau B spirit sol., R spirit sol 92

EchtbraunN 57

Echtgrttn 71

(1, SolidgrUn O in Teig)

Echtrot A, AV, 0 63

Echtrot B, P extra 64

Emerald green cryst 71

Eosine bleuatre, bluish 104

Eosin, B extra, DH, extra water sol., G,
G extra, GGF, 2G, I yellowish, J
extra, JJF, 3J, 4J extra, KS ord., MP,
OO extra, S extra yellowish, yellowish,

Y extra 103

Eosin B, BN, BW, DHV, I blfiulich, S

extra bluish 115

Eosin J 104

Eosin methylene blue 134

Eosin scarlet, B, BB extra 115

Erythrosin B, bluish, extra bluish, D,

J extra, JNV, W extra 104

Ethyl green 73, 76

Ethyl orange 42

Ethyl red 51

Ethyl purple 6B 75

Ethyl violet 75

Fast brown N 57

Fast pink for silk 91

Fast red A 63

Fast red B, P extra 64

Fast red cone 63

Fluorescein 106

Formanck's indicator 86

Fuchsia 89

Fuchsin acid 84

Fuchsin base 78

Fuchsin, 6B, crystals, FCOO, la cryst.,

NB, NG, RFN, VI cryst., XL 78

Fuchsin S, SIII, SN, SS, ST 84

Fustic 72, 84

Galleln, paste A, SW, W paste and powder 102

Gentian violet 137

Gold orange 60

Gold orange MP 41

Gold yellow 3, 65

Green crystals 71

Guernsey blue 80

Guaiac tincture 149

Hematein; Hematoxylin 136

Helianthin 36, 41

(141, Azogelb SG cone.)

Helianthin 1 156

Helianthin II 158

* The term curcumein has been applied to several different compounds.

CHOICE OF INDICATORS

TABLE 20— Continued

Helvetia blue 83

Henderson and Forbes' indicator 5

Hof mann's violet 72

Indigen D, F 92

Indigo carmine, carmine D paste, disul-

fonate, extract 100

Indigos Table 16

Indigotine la powder 100

Indophenin extra 92

Indulin base, 2B, BA, opal, spirit soluble,

RA 92

Iodeosin B 104

Iodine green 74

Jaune beurre 37

Jaune chrome R 61

Jaune d'aniline 30

Jaune d'or 3

Jaune II 65

Jaune M, mfitanile extra 230 23

Jaune naphtol 3

(7, Naphtolgelb S)

Iodeosin B 104

Todviolett 72

Kaiserrot 115

Kosmosrot extra 68

Kristallorange GG 66

jacmosol 142

'-.acmoid 143

jacmus 144

.lichtblau G 80

.light green N 71

.litmus 144

.ogwood 136

juck's indicator 113

iUnge's indicator 41

: ,yddit 1

. ivgosine 150

] fagdala red 91

1 [agenta 78

] [alachite green, A cryst., B, cryst. extra,
cryst. 3, cryst. 4, powder superfine B,

4B 71

I Calachite green G 73

1 "anchester yellow. 3

1 landarin G 60

1 !arine blue V 80

I artius yellow 3

I auvein 90

J elinite 1

J ellet's indicator 58

J etachrome orange R 62

J etanil yellow, extra, GR extra cone,

O, PL 23

I ethyl blue, for cotton, MBJ, MLB 83

J ethylene violet BN powder, RRA,

RRN, 3RA extra 89

J ethyl eosin B extra 115

Methyl green 76

Methyl orange, MP 41

Methyl red 50

Methyl violet 5B, 6B, 6B extra, 7B, 10B. . 77

Methyl water blue 83

Mimosa extract , 151

Miscellaneous indicators Table 19

Naphthalene red, rose 91

Naphthalene yellow 3

a-naphthol benzein 154

a-naphthol orange 59

Naphthol orange 59

Naphthol yellow 3

(7, Naphtolgelb S)

Naphthylamin brown 57

Naphthylamin pink 91

Naphthylamin yellow 3

Natural indicators Table 19

Neutral blue 94

Neutral red, extra 93

New green, cryst., BI, BII, Bill, GI,

Gil, GUI 71

New Victoria green I, II, 0 71

New yellow extra 25

Nicholson's blue 82

Nierenstein's indicator 139

Nile blue A, B, R 88

Nile blue 2B 87

Nitramine (?) 13

Nitro compounds, Nitro-phenols Table 8

NopalinG 115

Oil yellow 37

(36, Sudan I)

Opal blue bluish 80

Orange A 60

Orange B 59

Orange extra 60

Orange G 60, 66

(36, Sudan I)

Orange GG, GG in cryst., GMP 66

Orange GS, IV 25

Orange 1 59

Orange II, IIB, IIP, IIPL 60

Orange III 36, 41

Orange MN, MNO 23

Orange N 25

(79, Brillantorange R)

Orange No. 1 59

Orange No. 2 60

Orange No. 3 36, 41

Orange No. 4 25

Orange P 60

Orange R 62

(39, Ponceau G; 151, Orange T)

Orange R extra 59, 60

Orange S 59

Orangd au chrome 62

THE DETERMINATION OP HYDROGEN IONS

TABLE 20— Concluded

Orcein; Orchil 147

Orcellin No. 4 63

Orseille, carmine, extract 147

Oxazine compounds Table 13

Para methyl red 20

Paris violet 6B, 7B 77

Patent orange 66

Perkin's violet 90

Phenacetolin 141

Phenol red 125

Phenolphthaleins Table 17

Phenolsulfonphthaleins Table 18

Phloxin red BH 105

Phthaleins Table 17

i-picramic acid 8

Picric acid 1

Poirrier's blue 157

Poirrier's orange II 60

Pourpre francaise 147

Primerose soluble 104

Primula R water sol 72

Propyl red 52

Purpurin ' 96

Pyrosin B '. 104

Quinoline blue 85

Quinoline compounds Table 12

Red cabbage 138

Red violet, 5R extra 72

Red violet 5RS 79

Redwood 148

Resorcin yellow 65

Rhodamine B, B extra, 0 101

Roccellin 63

Rosanilin base 78

Rose B a l'eau 104

Rosein 78

Rose magdala 91

Rosolane 90

Rosolic acid 81

Rouge B 64

Rouge 1 63

Rouge congo '. 68

Rouge coton G, direct C 68

Rouge neutre extra 93

Rubidin 63

Rubin 78

Safranin 135

Safranin extra bluish 89

Safrosin 115

Saure gelb cryst., D extra, DMP 25

Saure orange. 60

Silk blue, BTSL 80

Smaragdgrun cryst 73

Solid blue base, B spirit sol., RR 92

Solid green J, JJO 73

Solid green 4B, cryst. A No. 1, cryst. O,

cryst. OO, extra J, O, OOJ, P 71

Soluble blue 80

(687, Methylblau fur Seide MLB)

Spirit induline, B, R cone 92

Spirit yellow, G 30

Sudan red 91

Sulfonphthaleins Table 18

Terra cotta R 62

Tymol blue 118

Tournesol 144

Triphenylme thane dyes Table 1 1

Troger and Hille's indicator 140

Tropaeolin G 23, 59

Tropaeolin O 65

Tropaeolin OO 25

Tropaeolin OOO No. 1 59

Tropaeolin OOO No. 2 60

Tropaeolin R 65

Turmeric 152

Uranin 106

Vert brillant 73'

Vert diamond P extra 71

Vert ethyle extra 73

Vert J3E, solide B extra, LB extra, solide

cristaux 0 71

Victoria yellow O double cone 23

Violet 5B, 6B, 7B 77

Violet 7B extra 70

Violet au bichromate 90

Violet benzyle 77

Violet C, G 70

Violet Hofmann 72

Violet meHhyl 6B, 6B extra cone 77

Violet pate 90

Violett R, RR, 4RN 72

Von M tiller's indicator 25

Walkorange R 62

Water blue, B, BJJ, R 80

Wool blue 83

Xanthone compounds Table 17

Yellow corallin 81

CHAPTER VI
Standard Buffer Solutions for Colorimetric Comparison

The standard solutions used in the colorimetric method of
determining hydrogen ion concentrations are buffer solutions with
such well defined compositions that they can be accurately repro-
duced, and with pH values accurately defined by hydrogen elec-
trode measurements. They generally consist of mixtures of some
acid and its alkali salt. Several such mixtures have been care-
fully studied. An excellent set has been described by S.^rensen
(1912). This set may be supplemented by the acetic acid —
sodium acetate mixtures, most careful measurements of which
have been made by Walpole (1914), and by Palitzsch's (1915)
excellent boric acid-borax mixtures.

Clark and Lubs (1916) have designed a set of standards which
they believe are somewhat more conveniently prepared than
are the S0rensen standards. Their set is composed of the follow-
ing mixtures:

Potassium chlorid + HC1
Acid potassium phthalate + HC1
Acid potassium phthalate + NaOH
Acid potassium phosphate + NaOH
Boric acid, KC1 + NaOH

For a discussion of these mixtures, the methods used in deter-
mining their pH values, and the potential measurements we refer
ihe reader to the original paper {Journal of Biological Chemistry,
1916, 25, no. 3, p. 479). We may proceed at once to describe the
letails of preparation.

The various mixtures are made up from the following stock solu-
tions: M/5 potassium chlorid (KC1), M/5 acid potassium phos-
)hate (KH2P04), M/5 acid potassium phthalate (KHC8H404),
Vl/5 boric acid with M/5 potassium chlorid (H3BO3, KC1), M/5
odium hydroxid (NaOH), and M/5 hydrochloric acid (HC1).
Uthough the subsequent mixtures are diluted to M/20 the above
oncentrations of the stock solutions are convenient for several
easons.

100 THE DETERMINATION OF HYDROGEN IONS

The water used in the crystallization of the salts and in the
preparation of the stock solutions and mixtures should be redis-
tilled. So-called "conductivity water," which is distilled first
from acid chromate solution and again from barium hydroxid, is
recommended, but it is not necessary.

M/5 potassium chlorid solution. (This solution will not be
necessary except in the preparation of the most acid series of
mixtures.) The salt should be recrystallized three or four times
and dried in an oven at about 120°C. for two days. The fifth
molecular solution contains 14.912 grams in 1 liter.

M/5 acid potassium phthalate solution. Acid potassium phtha-
late may be prepared by the method of Dodge (1915) modified
as follows. Make up a concentrated potassium hydroxid solu-
tion by dissolving about 60 grams of a high-grade sample in
about 400 cc. of water. To this add 50 grams of the commer-
cial resublimed anhydrid of ortho phthalic acid. Test a cool por-
tion of the solution with phenol phthalein. If the solution is still
alkaline, add more phthalic anhydrid; if acid, add more KOH.
When roughly adjusted to a slight pink with phenol phthalein1
add as much more phthalic anhydrid as the solution contains and
heat till all is dissolved. Filter while hot, and allow the crystal-
lization to take place slowly. The crystals should be drained
with suction and recrystallized at least twice from distilled water.2

Crystallization should not be allowed to take place below
20°C, for Dodge (1920) states:

A saturated solution of the acid phthalate on chilling will deposit
crystals of a more acid salt, having the formula 2KHC8H404-C8Hg04.
These crystals are in the form of prismatic needles, easily distinguished
under the microscope from the 6-sided orthorhombic plates of the salt
KHCH4O4.

Dry the salt at 110°-115°C. to constant weight.

A fifth molecular solution contains 40.836 grams of the salt in
1 liter of the solution.

M/5 acid potassium phosphate solution. A high-grade com-
mercial sample of the salt is recrystallized at least three times

1 Use a diluted portion for the final test.

2 Samples of phthalic anhydrid which are now found on the market are
frequently grossly impure. With some samples ten recrystallizations
are necessary. Hence it is economy to purchase only the highest grades.

STANDARD BUFFER SOLUTIONS 101

from distilled water and dried to constant weight at 110°-115°C.
A fifth molecular solution should contain in 1 liter 27.232 grams.
The solution should be distinctly red with methyl red and dis-
tinctly blue with brom phenol blue.

M/5 boric acid, M/5 potassium chlorid. Boric acid should be
recrystallized several times from distilled water. It should be
air dried3 in thin layers betweeri filter paper and the constancy
of weight established by drying small samples in thin layers in a
desiccator over CaCl2. Purification of KC1 has already been
noted. It is added to the boric acid solution to bring the salt
concentration in the borate mixtures to a point comparable with
that of the phosphate mixtures so that colorimetric checks may
be obtained with the two series where they overlap. One liter
of the solution should contain 12.40484 grams of boric acid and
14.912 grams of potassium chlorid.

M/5 sodium hydroxid solution. This solution is the most diffi-
cult to prepare, since it should be as free as possible from carbon-
ate. A solution of sufficient purity for the present purposes may
be prepared from a high grade sample of the hydroxid in the
following manner. Dissolve 100 grams NaOH in 100 cc. distilled
water in a Jena or Pyrex glass Erlenmeyer flask. Cover the
mouth of the flask with tin foil and allow the solution to stand
over night till the carbonate has settled. Then prepare a filter
as follows. Cut a "hardened " filter paper to fit a Buchner funnel.
Treat it with warm, strong [1:1] NaOH solution. After a few
minutes decant the sodium hydroxid and wash the paper first
with absolute alcohol, then with dilute alcohol, and finally with
large quantities of distilled water. Place the paper on the Buch-
ner funnel and apply gentle suction until the greater part of the
water has evaporated; but do not dry so that the paper curls.
Now pour the concentrated alkali upon the middle of the paper,
spread it with a glass rod making sure that the paper, under
gentle suction, adheres well to the funnel, and draw the solution

* Boric acid begins to lose "water of constitution" above 50°C.

* This weight was used on the assumption that the atomic weight of
boron is 11.0. The atomic weight has since been revised and appears as
10.9 in the 1920 table.

Because the solutions were standardized with the above weight of boric
icid this weight should be used.

102 THE DETERMINATION OF HYDROGEN IONS

through with suction. The clear filtrate is now diluted quickly,
after rough calculation, to a solution somewhat more concentrated
than N/1. Withdraw 10 cc. of this dilution and standardize
roughly with an acid solution of known strength, or with a sample
of acid potassium phthalate. From this approximate standardi-
zation calculate the dilution required to furnish an M/5 solution.
Make the required dilution with the least possible exposure, and
pour the solution into a paraffined5 bottle to which. a calibrated 50
cc. burette and soda-lime guard tubes have been attached. The
solution should now be most carefully standardized. One of the
simplest methods of doing this, and one which should always be
used in this instance, is the method of Dodge (1915) in which use
is made of the acid potassium phthalate purified as already
described. Weigh out accurately on a chemical balance with
standardized weights several portions of the salt of about 1.6 grams
each. Dissolve in about 20 cc. distilled water and add 4 drops
phenol phthalein. Pass a stream of C02-free air through the
solution and titrate with the alkali till a faint but distinct and
permanent pink is developed. It is preferable to use a factor
with the solution rather than attempt adjustment to an exact
M/5 solution.

If one should be fortunate enough to find that the concentrated
sodium hydroxid solution had clarified itself without leaving
suspended carbonate, the clear solution might be carefully pi-
petted from the sediment. Cornog (1921) describes another
method as follows:

Distilled water contained in an Erlenmeyer flask is boiled to remove
any carbon dioxide present, after which, when the water is cooled enough,
ethyl ether is added to form a layer 3 or 4 cm. in depth. Pieces of metallic
sodium, not exceeding about 1 cm. in diameter are then dropped into the
flask. They will fall no further than the ether. layer where they remain
suspended. The water contained in the ether layer causes the slow forma-
tion of sodium hydroxid, which readily passes below to the water layer.

8 The author finds that thick coats of paraffine are more satisfactory than
the thin coats sometimes recommended. Thoroughly clean and dry the
bottle, warm it and then pour in the melted paraffine. Roll gently to make
an even coat and just before solidification occurs stand the bottle upright
to allow excess paraffine to drain to the bottom and there form a very sub-
stantial layer.

STANDARD BUFFER SOLUTIONS 103

Cornog depends upon the evaporation of the ether as a barrier
to CO2. There are various ways in which the protection can be
made more sure, and there are also various ways in which the
aqueous solution may be separated from the ether.

From time to time there appear in the literature suggestions
regarding the use of barium salts to remove the carbonate in
alkali solutions.

In the author's opinion the next step to take, if the separation
of carbonate from very concentrated NaOH solutions is not con-
sidered refined enough for the purpose at hand, is to proceed
directly to the electrolytic preparation of an amalgam. Given
a battery and two platinum electrodes this is a simple process.
A deep layer of redistilled mercury is placed in a conical separa-
tory funnel. The negative pole of the battery is led to this
mercury by a glass-protected platinum wire. Over the mercury
is placed a concentrated solution of recrystallized sodium
chlorid and in this solution is dipped a platinum electrode con-
nected with the positive pole of the battery. The battery may
be 4 to 6 volts. Electrolysis is continued with occasional gentle
shaking to break up amalgam crystals forming on the mercury
surface.

Boil the CO2 out of a litre or so of redistilled water, and, while
steam is still escaping, stopper the flask with a cork carrying a
siphon, a soda-lime guard tube and a corked opening for the
separatory funnel.

When the water is cool introduce the delivery tube of the separa-
tory funnel and deliver the amalgam. Allow reaction to take
place till a portion of the solution, when siphoned off to a
burette and standardized, shows that enough hydroxid has been
formed. Then siphon approximately the required amount into a
boiled-out and protected portion of water. Mix thoroughly and
standardize.

M/5 hydrochloric acid solution. Dilute a high grade hydro-
chloric acid solution to about 20 per cent and distill. Dilute the
distillate to approximately M/5 and standardize with the sodium
hydroxid solution previously described. If convenient, it is well
to standardize this solution carefully by the silver chlorid method
and check with the standardized alkali.

104

THE DETERMINATION OF HYDROGEN IONS

|T^

D^-

v «r

Fig. 11. Clark and Lubs' Standard Mixtures

A. 50 cc. 0.2m KHPhthalate + X cc. 0.2m HC1. Diluted to 200 cc.

B. 50 cc. 0.2m KHPhthalate + X cc. 0.2m NaOH. Diluted to 200 cc.

C. 50 cc. 0.2m KH2PO< + X cc. 0.2m NaOH. Diluted to 200 cc.

D. 50 cc. 0.2m HsB03, 0.2m KC1 + X cc. 0.2m NaOH. Diluted to 200 cc.

STANDARD BUFFER SOLUTIONS 105

The only solution which it is absolutely necessary to protect
from the CO2 of the atmosphere is the sodium hydroxid solution.
Therefore all but this solution may be stored in ordinary bottles
of resistant glass. The salt solutions, if adjusted to exactly M/5,
may be measured from clean calibrated pipettes.

These constitute the stock solutions from which the mixtures
are prepared. The general relationships of these mixtures to
their pH values are shown in figure 11. In this figure pH values
are plotted as ordinates against X cc. of acid or alkali as abscissas.
It will be found advantageous to plot this figure from table 21 with
greatly enlarged scale so that it may be used as is S0rensen's
chart (1909). The compositions of the mixtures at even intervals
of 0.2 pH are given in table 21.

In any measurement the apportionment of scale divisions
should accord with the precision. Scale divisions should not be
so coarse that interpolations tax the judgment nor so fine as to
be ridiculous. What scale divisions are best in the method under
discussion it is difficult to decide, since the precision which may
be attained depends somewhat upon the ability of the individual
eye, and upon the material examined, as well as upon the means
and the judgment used in overcoming certain difficulties which
we shall mention later. S0rensen (1909) has arranged the stand-
ard solutions to differ by even parts of the components, a system
which furnishes uneven increments in pH. Michaelis, (1910)
on the other hand, makes his standards vary by about 0.3 pH
so that the corresponding hydrogen ion concentrations are approxi-
mately doubled at each step. Certain general considerations
lead to the conclusion that for most work estimation of pH values
to the nearest 0.1 division is sufficiently precise, and that this
precision can be obtained when the nature of the medium per-
mits if the comparison standards differ by increments of 0.2 pH.

It is convenient to prepare 200 cc. of each of the mixtures and
to preserve them in bottles each of which has its own 10 cc.
pipette thrust through the stopper. , It takes but little more time
to prepare 200 cc. than it does to prepare a 10 cc. portion, and
if the larger volume is prepared there will not only be a sufficient
quantity for a day's work but there will be some on hand for the
occasional test.

Unless electrometric measurements can be used as control, we

106

THE DETERMINATION OP HYDROGEN IONS

urge the most scrupulous care in the preparation and preserva-
tion of the standards. We have specified several recrystallizations
of the salts used because no commercial samples which we have
yet encountered are reliable.

TABLE 21

Composition of mixtures giving pH values at
KC1-HC1 mixtures*

\C. at intervals of 0.2

1.2

50 cc.

M/5 KC1

64.5 cc.

M/5 HC1

Dilute to 200 cc.

1.4

50 cc.

M/5 KC1

41.5 cc.

M/5 HC1

Dilute to 200 cc.

1.6

50 cc.

M/5 KC1

26.3 cc.

M/5 HC1

Dilute to 200 cc.

1.8

50 cc.

M/5 KC1

16.6 cc.

M/5 HC1

Dilute to 200 cc.

2.0

50 cc.

M/5 KC1

10.6 cc.

M/5 HC1

Dilute to 200 cc.

2.2

50 cc.

M/5 KC1

6.7 cc.

M/5 HC1

Dilute to 200 cc.

* The pH values of these mixtures are given by Clark and Lubs (1916)
as preliminary measurements.

Phthalate-HCl mixtures

2.2 50 cc. M/5 KHPhthalate 46 .70 cc. M/5 HC1 Dilute to 200 cc.

2.4 50 cc. M/5 KHPhthalate 39.60 cc. M/5 HC1 Dilute to 200 cc.

2.6 50 cc. M/5 KHPhthalate 32.95 cc. M/5 HC1 Dilute to 200 cc.

2.8 50 cc. M/5 KHPhthalate 26.42 cc. M/5 HC1 Dilute to 200 cc.

3.0 ' 50 cc. M/5 KHPhthalate 20.32 cc. M/5 HC1 Dilute to 200 cc.

3.2 50 cc. M/5 KHPhthalate 14.70 cc. M/5 HC1 Dilute to 200 cc.

3.4 50 cc. M/5 KHPhthalate 9.90 cc. M/5 HC1 Dilute to 200 cc.

3.6 50 cc. M/5 KHPhthalate 5 .97 cc. M/5 HC1 Dilute to 200 cc.

3.8 50 cc. M/5 KHPhthalate 2.63 cc. M/5 HC1 Dilute to 200 cc.

Phthalate-NaOH mixtures

4.0 50 cc. M/5 KHPhthalate 0.40 cc. M/5 NaOH Dilute to 200 cc.

4.2 50 cc. M/5 KHPhthalate 3.70 cc. M/5 NaOH Dilute to 200 cc.

4.4 50 cc. M/5 KHPhthalate 7.50 cc. M/5 NaOH Dilute to 200 cc.

4.6 50 cc. M/5 KHPhthalate 12.15 cc. M/5 NaOH Dilute to 200 cc.

4.8 50 cc. M/5 KHPhthalate 17.70 cc. M/5 NaOH Dilute to 200 cc.

5.0 50 cc. M/5 KHPhthalate 23.85 cc. M/5 NaOH Dilute to 200 cc.

5.2 50 cc. M/5 KHPhthalate 29.95 cc. M/5 NaOH Dilute to 200 cc.

5.4 50 cc. M/5 KHPhthalate 35.45 cc. M/5 NaOH Dilute to 200 cc.

5.6 50 cc. M/5 KHPhthalate 39.85 cc. M/5 NaOH Dilute to 200 cc.

5.8 50 cc. M/5 KHPhthalate 43.00 cc. M/5 NaOH Dilute to 200 cc.

6.0 50 cc. M/5 KHPhthalate 45.45 cc. M/5 NaOH Dilute to 200 cc.

6.2 50 cc. M/5 KHPhthalate 47.00 cc. M/5 NaOH Dilute to 200 cc.

STANDARD BUFFER SOLUTIONS

107

KH2P04-NaOH mixtures

5.8
6.0

6.2
6.4
6.6
6.8

7.0
7.2
7.4
7.6
7.8
8.0

50 cc
50 cc
50 cc
50 cc,
50 cc
50 cc,
50 cc,
50 cc,
50 cc
50 cc,
50 cc,
50 cc

M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04
M/5 KH2P04

3.72 cc.

5.70 cc.

8.60 cc.
12.60 cc.
17.80 cc.
23.65 cc.
29.63 cc.
35.00 cc.
39.50 cc.
42.80 cc.
45.20 cc.
46.80 cc.

M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH

Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute

to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.

Boric acid, KCl-NaOH mixtures

7.8 50 cc.
8.0 50 cc.
8.2 50 cc.
8.4 50 cc.
8.6 50 cc.
8.8 50 cc.
9.0 50 cc.
9.2 50 cc.
9.4 50 cc.
9.6 50 cc.
9.8 50 cc.
10.0 50 cc.

M/5 H3B03
M/5 H3BO3
M/5 H3B03
M/5 H3B03
M/5 H3B03
M/5 H3B03
M/5 H3B03
M/5 H3B03
M/5 H3B03
M/5 H3B03
M/5 H3B03
M/5 H3B03

M/5KC1 2
M/5KC1 3
M/5KC1 5
M/5KC1 8
M/5 KC1 12
M/5KC1 16
M/5 KC1 21
M/5KC126
M/5KC1 32
M/5 KC1 36
M/5 KC1 40
M/5 KC1 43

61 cc
97 cc
90 cc
50 cc
00 cc
30 cc
30 cc
70 cc
00 cc
85 cc
80 cc
90 cc

M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH

Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute

to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.

It is important to check the consistency of any particular set
of these mixtures by comparing "5.8" and "6.2 phthalate" with
"5.8" and "6.2 phosphate" using brom cresol purple. Also
"7.8" and "8.0 phosphate" should be compared with the corre-
sponding borates using cresol red.

S0rensen's standards are made as follows. The stock solutions
are: 4

1. A carefully prepared exact tenth normal solution of HC1.

2. A carbonate-free exact tenth normal solution of NaOH.

3. A tenth molecular glycocoll solution containing sodium chlo-
rid, 7.505 grams glycocoll and 5.85 grams NaCl in 1 litre of
solution.

4. An M/15 solution of primary potassium phosphate which
contains 9.078 grams KH2P04 in 1 litre of solution.

108

THE DETERMINATION OF HYDROGEN IONS

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Fia. 12. S0rensen's Standard Mixtures, Walpole's Acetate Solutions

AND PALITZSCH's BORATE SOLUTIONS

Mixtures of A parts of acid constituent and B parts of basic constituent.

STANDARD BUFFER SOLUTIONS 109

5. An M/15 solution of secondary sodium phosphate which
contains 11.876 grams Na2HP04,2H20 in 1 litre of solution.

6. A tenth molecular solution of secondary sodium citrate made
from a solution containing 21.008 grams crystallized citric acid
and 200 cc. carbonate-free N/1 NaOH diluted to 1 litre.

7. An alkaline borate solution made from 12.404 grams boric
acid dissolved in 100 cc. carbonate-free N/1 NaOH and diluted
to 1 litre.

The materials for these solutions are described by S0rensen as
follows.

The water shall be boiled, carbon dioxid-free, distilled water,
and the solutions shall be protected against contamination by
C02.

Glycocoll (Glycine)

Two grams glycocoll should give a clear solution in 20 cc.
water and should test practically free of chlorid or sulfate. Five
grams should yield less than 2 mgm. of ash. Five grams should
yield, on distillation with 300 cc. of 5 per cent sodium hydroxid,
less than 1 mgm. of nitrogen as ammonia. The nitrogen content
as determined by the Kjeldahl method should be 18.67 ±0.1 per
cent.

Primary phosphate, KH2PO4

The salt must dissolve clear in water and yield no test for chlo-
rid or for sulfate. When dried under 20 or 30 mm. pressure for
a day at 100°C. the loss in weight should be less than 0.1 per cent,
and on ignition the loss should be 13.23 ±0.1 per cent. When
compared colorimetrically with citrate mixtures the stock phos-
phate solution should lie between "7" and "8 citrate-HCl." On
addition of a drop of tenth-normal alkali or acid to 100 cc. the
color of this phosphate solution with an indicator should be
widely displaced.

Secondary phosphate, Na2HP04, 2H20

The salt with this content of water of crystallization is pre-
pared by exposing to the ordinary atmosphere the crystals con-

110 THE DETERMINATION OF HYDROGEN IONS

taining twelve mols of water.6 About two weeks exposure is
generally sufficient. The salt should dissolve clear in water and
yield no test for chlorid or sulfate. A day of drying under 20 to
30 mm. pressure at 100°C. and then careful ignition to constant
weight, should result in a 25.28 ± 0.1 per cent loss. The stock
solution should correspond on colorimetric test with "10 borate-
HC1" and should be displaced beyond "8 borate-HCl" on addi-
tion of a drop of N/10 acid, and beyond "8 borate-NaOH " with
a drop of alkali to 100 cc.

Citric acid, C6H807,H20

The acid should dissolve clear in water, should yield no test for
chlorid or sulfate and should give practically no ash. The water
of crystallization may be determined by drying under 20 to 30
mm. pressure at 70° C. On drying in this manner the acid should
remain colorless and lose 8.58 ± 0.1 per cent. The acidity of the
citric acid solution is determined by titration with 0.2 N barium
hydroxid with phenolphthalein as indicator. Titration is carried
to a distinct red color of the indicator.

Boric acid, H3B03

Twenty grams of boric acid should go completely into solution
in 100 cc. of water when warmed on a strongly boiling water bath.
This solution is cooled in ice water and the filtrate from the crys-
tallized boric acid is tested as follows. It should give no tests for
chlorides or sulfates. It should be orange to methyl orange. A
drop of N/10 HC1 added to 5 cc. should make the filtrate red
to methyl orange. Twenty cubic centimeters of the filtrate evap-
orated in platinum, treated with about 10 grams of hydrofluoric
acid and 5 cc. of concentrated sulfuric acid and reevaporated,
ignited and weighed, should yield less than 2 mgm. when corrected
for non-volatile matter in the HF.

fne following tables give the S0rensen mixtures with the cor-
responding pH values. Mixtures whose pH values are consid-

• Certain samples of secondary sodium phosphate sold for the prepa-
ration of buffer standards and called "S0rensen's Phosphate" are wrongly
labeled Na2HP04.

STANDARD BUFFER SOLUTIONS

111

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9.5 Glycine + 0.5 NaOH
9.0 Glycine + 1.0 NaOH
8.0 Glycine + 2.0 NaOH
7.0 Glycine + 3.0 NaOH

6.0 Glycine + 4.0 NaOH
5.5 Glycine + 4.5 NaOH

5.1 Glycine + 4.9 NaOH
5.0 Glycine + 5.0 NaOH
4.9 Glycine + 5.1 NaOH
4.5 Glycine + 5.5 NaOH
4.0 Glycine + 6.0 NaOH
3.0 G lycine + 7.0 NaOH
2.0 G lycine + 8.0 NaOH
1.0 G lycine + 9.0 NaOH

112

THE DETERMINATION OF HYDROGEN IONS

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TABLE 24
Stfrensen's borate — HCl mixtures after W album

10°

20°

30°

40°

50°

60°

70°

10.0 Borate

9.30
9.22

9.23
9.15

9.15

9.08

9.08
9.01

9.00
8.94

8.93

8.87

8.86

9.5 Borate + 0.5 HCl

8.80

9.0 Borate + 1.0 HCl

9.14

9.07

9.01

8.94

8.87

8.80

8.74

8.5 Borate + 1.5 HCl

9.06

8.99

8.92

8.86

8.80

8.73

8.67

8.0 Borate + 2.0 HCl

8.96

8.89

8.83

8.77

8.71

8.65

8.59

7.5 Borate + 2.5 HCl

8.84

8.79

8.72

8.67

8.61

8.55

8.50

7.0 Borate + 3.0 HCl

8.72

8.67

8.61

8.56

8.50

8.45

8.40

6.5 Borate + 3.5 HCl

8.54

8.49

8.44

8.40

8.35

8.30

8.26

6.0 Borate + 4.0 HCl

8.32

8.27

8.23

8.19

8.15

8.11

8.08

5.75 Borate + 4.25 HCl...

8.17

8.13

8.09

8.06

8.02

7.98

7.95

5.5 Borate + 4.5 HCl

7.96

7.93

7.89

7.86

7.82

7.79

7.76

5.25 Borate + 4.75 HCl...

7.64

7.61

7.58

7.55

7.52

7.49

7.47

TABLE 25
Sflrensen's citrate — NaOH mixtures after Walbum

Temperature.

10.0 Citrate

9.5 Citrate + 0.5 NaOH..
9.0 Citrate + 1.0 NaOH..
8.0 Citrate + 2.0 NaOH..
7.0 Citrate + 3.0 NaOH..
6.0 Citrate + 4.0 NaOH..
5.5 Citrate + 4.5 NaOH..
5.25 Citrate + 4.75 NaOH

10°

20°

30°

4C°

50°

60°

4.93

4.96

5.00

5.04

5.07

5.10

4.99

5.02

5.06

5.10

5.13

5.16

5.08

5.11

5.15

5.19

5.22

5.25

5.27

5.31

5.35

5.39

5.42

5.45

5.53

5.57

5.60

5.64

5.67

5.71

5.94

5.98

6.01

6.04

6.08

6.12

6.30

6.34

6.37

6.41

6.44

6.47

6.65

6.69

6.72

6.76

6.79

6.83

70°

5.14
5.20
5.29
5.49
5.75
6.15
6.51
6.86

TABLE 26
irensen's glycocoll — HCl mixtures

GLYCOCOLL

HCl

CC. ,

CC.

0.0

10.0

1.038

1.0

9.0

1.146

2.0

8.0

1.251

3.0

7.0

1.419

4.0

6.0

1.645

5.0

1.932

6.0

4.0

2.279

7.0

3.0

2.607

8.0

2.0

2.922

9.0

1.0

3.341

9.5

. 0.5

3.679

113

114

THE DETERMINATION OF HYDROGEN IONS

TABLE 27

irensen's phosphate mixtures

SECONDARY

PRIMARY

CC.

0.25

9.75

5.288

0.5

9.5

5.589

1.0

9.0

5.906

2.0

8.0

6.239

3.0

7.0

6.468

4.0

6.0

6.643

5.0

6.813

6.0

4.0

6.979

7.0

3.0

7.168

8.0

2.0

7:381

9.0

1.0

7.731

9.5

0.5

8.043

TABLE 28
S0rensen's citrate — HCl mixtures

CITRATE

HCl

CC.

0.0

10.0

1.038

1.0

9.0

1.173

2.0

8.0

1.418

3.0

7.0

1.925

3.33

6.67

2.274

4.0

6.0

2.972

4.5

5.5

3.364

4.75

5.25

3.529

5.0

3.692

5.5

4.5

3.948

6.0

4.0

4.158

7.0

3.0

4.447

8.0

2.0

4.652

9.0

1.0

4.830

9.5

0.5

4.887

10.0

0.0

4.958

STANDARD BUFFER SOLUTIONS

115

TABLE 29

Walpole's acetate buffer mixtures, recalculated for intervals of 0.2 pH.
acetate 0.2 molecular

Total

CONCENTRATION (MOLALITY)

Acetic Acid

Sodium acetate

3.6
3.8

4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6

0.185
0.176
0.164
0.147
0.126
0.102
0.080
0.059
0.042
0.029
0.019

0.015
0.024
0.036
0.053
0.074
0.098
0.120
0.141
0.158
0.171
0.181

TABLE 30

Palitzsch's borax-boric acid mixtures

M/20 BORAX

M/5 boric acid, M/20 NaCl

cc.

10.0

0.0

9.24

9.0

1.0

9.11

8.0

2.0

8.98

7.0

3.0

8.84

6.0

4.0

8.69

5.5

4.5

8.60

5.0

8.51 '

4.5

5.5

8.41

4.0

6.0

8.31

3.5

6.5

8.20

3.0

7.0

8.08

2.5

7.5

7.94

2.3

7.7

7.88

2.0

8.0

7.78

1.5

8.5

7.60

1.0

9.0

7.36

0.6

9.4

7.09

0.3

9.7

6.77

116

THE DETERMINATION OF HYDROGEN IONS

ered by S0rensen to be too uncertain and which he has indicated
by brackets are omitted in these tables. The third decimal of
S0rensen's tables are given by S0rensen in small type.

TABLE 31
Mcllvaine's standards

pH REQUIRED

0.2MNa2HPO<

0.1 M CITRIC ACID

cc.

CC.

2.2

0.40

19.60

2.4

1.24

18.76

2.6

2.18

17.82

2.8

3.17

16.83

3.0

4.11

15.89

3.2

4.94

15.06

3.4

5.70

14.30

3.6

6.44

13.56

3.8

7.10

12.90

4.0

7.71

12.29

4.2

8.28

11.72

4.4

8.82

11.18

4.6

9.35

10.65

4.8

9.86

10.14

5.0

10.30

9.70

5.2

10.72

9.28

5.4

11.15

8.85

5.6

11.60

8.40

5.8

12.09

7.91

6.0

12.63

7.37

6.2

13.22

6.78

6.4

13.85

6.15

6.6

14.55

5.45

6.8

15.45

4.55

7.0

16.47

3.53

7.2

17.39

2.61

7.4

18.17

1.83

7.6

18.73

1.27

7.8

19.15

0.85

8.0

19.45

0.55

Walbum (1920) has determined the pH values for the S0ren-
sen mixtures at temperatures of 10°, 18°, 28°, 37°, 46°, 62° and
70°C. and has interpolated data for intervening temperatures.
He uses a system of reference essentially that which is described

STANDARD BUFFER SOLUTIONS 117

in Chapter XIX as standard. He finds that upon this basis the
alteration of pH with temperature is for the most part negligible
for the phosphate mixtures, the glycocoll-HCl mixtures and the
citrate-HCl mixtures. Data for the other mixtures are tabu-
lated in tables 22, 23, 24 and 25. In these will be found S0ren-
sen's values at 18°. Tables 26, 27 and 28 are taken from
S0rensen's paper of 1912.

The stock solutions for the Palitzsch mixtures given in table 30
are an M/20 Borax solution containing 19.108 grams7 Na2B407
10H2O in 1 litre; and an M/5 Boric acid, NaCl solution contain-
ing 12.404 grams7 H3B03 and 2.925 grams NaCl in 1 litre.

Mcllvaine (1921) has given the electrometrically determined
pH values for a series of mixtures of 0.2 M disodium phosphate
and 0.1 M citric acid. Since the citrate exerts a buffer action
at the steep part of the phosphate curve near the position where
the mono alkali phosphate alone is present Mcllvaine's mixtures
give a continuous buffer action from pH 2.2 to pH 8.0. His data
are shown in table 31.

Acree and his coworkers have published curves for other mix-
tures giving more or less smooth slopes over wide ranges of pH.

Kolthoff in his 1921 text has recalculated the follow, ing data
from Ringer (1909):

TABLE 32
Ringer's mixtures of 0.15M Na2HPOi and 0.1M NaOH

50 cc. Na2HP04 + 15 cc. NaOH.
50 cc. Na2HP04 + 25 cc. NaOH.
50 cc. Na2HP04 + 50 cc. NaOH.
50 cc. Na2HP04 + 75 cc. NaOH.

10.97
11.29
11.77
12.06

7 The values given by Palitzsch were calculated upon the basis of 11.0
as the atomic weight of boron. Since this was the value used, the new
value of 10.9 given in the atomic weight table in 1 he report of the inter-
national committee for 1922 should not be used in calculating the composi-
tion of the specific solutions given by Palitzsch.

CHAPTER VII

Sources of Error in Colorimetric Determinations

There are errors of technique such as incorrect apportionment
of the indicator concentration in tested and standard solution and
the use of unequal depths of solutions through which the colors
are viewed that may be passed over with only a word of reminder.
Likewise we may recall certain of the optical effects mentioned
in Chapter IV and then pass on to the more serious difficulties
in the application of the indicator method.

In the comparison of electrometric and colorimetric measure-
ments discrepancies have often been traced so clearly to two defi-
nite sources of error that they have been given categorical dis-
tinction. They are the so-called "protein" and "salt" errors.

From what has already been said in previous pages, it will
be seen that, if there are present in a tested solution bodies which
remove the indicator or its ions from the field of action either by
adsorption , or otherwise, the equilibria which have formed the
basis of our treatment will be disturbed. An indicator in such a
solution may show a color intensity, or even a quality of color,
which is different from that of the same concentration of the indi-
cator in a solution of the same hydrogen ion concentration where
no such disturbance occurs. We could easily be led to attribute
very different hydrogen ion concentrations to the two solutions.
This situation is not uncommon when we are dealing with protein
solutions, for in some instances there is distinctly evident the re-
moval of the indicator from the field. In other cases the discrep-
ancy between electrometric and colorimetric measurements is not
so clear, nor can it always be attributed solely to the indicator
measurement.

If two solutions of inorganic material, each containing the same
concentration of hydrogen ions,' are tested with an indicator, we
should expect the same color to appear. If, however, these two
solutions have different concentrations of salt, it may happen that
the indicator color is not the same. As S0rensen (1909) and
Scfrensen and Palitzsch (1913) have demonstrated, this effect of

118

ERRORS IN COLORIMETR1C DETERMINATIONS

119

the salt content of a solution cannot be tested by adding the salt
to one of two solutions which have previously been brought to
the same hydrogen ion concentration. The added salt, no matter
if it be a perfectly neutral salt, will change either the hydrogen
ion concentration or the hydrogen ion activity of the solution or
so affect the electrode equilibrium that it appears as if the hydro-
gen ion activity is altered.

So long as hydrogen electrode measurements are made the
standard it is convenient to throw the burden of the "salt effect"
upon the indicator; but neutral salts are known to displace elec-
trode potential differences from the point estimated from the
expected hydrogen ion concentration. Tentatively we may deal
with the salt effect as if the hydrogen electrode measurement
were the point of reference, and this will doubtless harmonize
with future developments of theory.

Bjerrum (1914) gives an example of a case where the influence
}f the neutral salt is evidently upon the buffer equilibrium rather
;han on the indicator. An ammonium-ammonium salt buffer
nixture and a borate buffer mixture are both made up to the
name color of phenolphthalein. On the addition of sodium chlo-
ride the color of phenolphthalein becomes stronger in the ammo-
nium mixture and weaker in the borate mixture.

The following table taken from Prideaux (1917) illustrates the
order of magnitude of the "salt error" in some instances.

INDICATOR

] ara benzene sulphonic acid azo naphthylamine.

I ara nitro phenol

/ lizarine sulphonic acid

1 eutral red

I osolic acid

I ara benzene sulphonic acid azo a-naphthol . . .
I henolphthalein

BUFFER USED

Phosphate
Phosphate
Phosphate
Phosphate
Phosphate
Phosphate
Phosphate

CHANGE OF pH

IN PRESENCE OF

0.5 N NaCl

-0.10
+0.15
+0.26
-0.09
+0.08
+0.12
+0.12

\ In cases where the solutions under examination are of the same
g meral nature hydrogen electrode measurements may be taken as
t te standard and colorimetric measurements calibrated accord-
i gly. S0rensen and Palitzsch (1910) did this in their study of

120

THE DETERMINATION OF HYDROGEN IONS

the salt errors of indicators in sea water. They acidified the sea
water and passed hydrogen through to displace carbon dioxid,
and then neutralized it to the ranges of various indicators with
buffer mixtures and compared colorimetric with electrometric
measurements. In this way they found the following deviations.

INDICATOR

BUFFER

PARTS PER 1000 OF SALTS AND
CORRESPONDING ERRORS

Faranitro phenol

Phosphate

Borate

Phosphate

Borate

+0.12
-0.10
+0.22
+0.16
+0.21

+0.08
-0.05
+0.17
+0.11
+0.16

+0.03
-0.04
+0.05

Neutral red

a-Napththol phthalein..\
Phenolphthalein

-0.07
-0.14
-0.03

If, for example, sea water of about 3.5 per cent salt is matched
against a standard borate solution with phenolphthalein and
appears to be pH 8.43 the real value is pH 8.22.

Such calibration is doubtless the very best way to deal with the
salt errors since it tends to bring measurements to a common
experimental system of reference.

Kolthoff (1922) gives the following table showing the correc-
tions to be applied for the "salt error" of various indicators. It
should be noted that Kolthoff includes in this table data obtained
when the hydrogen electrode potentials were taken as standard
and also data in which the pH values were calculated. The two
sets are not strictly comparable (see Chapter XIX) and there-
fore must be used with caution in theoretical work. We have
eliminated from Kolthoff's table Congo red, Azolitmin, and
Tropaeolin O (Chrysom) which Kolthoff describes as having
salt errors so large that these indicators are useless.

Michaelis and his coworkers have determined the salt errors
for a number of the nitrophenols, but, since the corrections are
often intimately related to the constants used in Michaelis*
method of operating, the reader is referred to the original litera-
ture for the details. See Chapter VIII.

The reader was warned in Chapter II that the treatment to be
given the so-called salt errors of indicators would not deal with the
theory. There are various theories that have been advanced,

TABLE 33

Salt error of indicators, after Kolthoff

INDICATOR

Tropaeolin 00
(Orange IV)

Methyl orange
Butter yellow. .

Thymol blue (acid
range)

Brom phenol blue <

Brom cresol purple.
Phenol red

Thymol blue

Methyl red

p-Nitro phenol.. .
Azo yellow 3G. . .
Phenolph thalein .

Nitramine (?)...

SALT

SALT
CONCEN-
TRATION

CORREC-
TION

KC1

0.10 N

-0.05

KC1

0.25 N

-0.01

KC1

0.50 N

+0.06

KC1

1.00 N

+0.23

KC1

0.10 N

-0.08

KC1

0.25 N

-0.08

KC1

0.50 N

+0.02

KC1

1.00 N

+0.23

KC1

0.10 N

-0.08

KC1

0.10 N

-0.06

KC1

0.20 N

-0.06

KC1

0.50 N

-0.04

KC1

1.00 N

+0.05

KC1

0.10 N

-0.05

KC1

0.25 N

-0.15

KC1

0.50 N

-0.35

KC1

1.00 N

-0.35

NaCl

0.50 N

-0.25

NaCl

0.50 N

-0.15

NaCl

0.50 N

-0.17

NaCl

0.50 N

+0.10

NaCl

0.50 N

-0.05

NaCl

0.50 N

0.00

NaCl

0.50 N

-0.17

KC1

0.10 N

-0.06

KC1

0.25 N

-0.12

KC1

0.50 N

-0.10

KC1

1.00 N

-0.29

REMARKS

Indicator suitable. NaCl
has about same influence

Same errors as methyl
orange but indicator floc-
culates with salt

NaCl has same influence

Corrections large at weaker
concentration of salt

At small concentrations of
salt correction of opposite
sign

NaCl has about same influ-
ence

121

122 THE DETERMINATION OF HYDROGEN IONS

but up to a recent time none has been entirely satisfactory.
Whether the newer concepts of the conduct of strong electrolytes
will furnish a basis for the correlation of experimental data remains
to be seen. This much at least will be demanded, that the habit
of indiscriminately jumbling together dissociation constants and
other data obtained by widely different methods and bearing
different implications shall cease. Until a thoroughly consistent
method of approach and of calculation is accomplished and its
value established, the only safe procedure to follow is to calibrate
salt errors by experimental hydrogen electrode measurements.

In dealing with protein solutions calibration is less certain.
When solutions to be tested vary greatly, not only in protein con-
tent but also in the composition and concentration of their salt
content, systematic calibration becomes very difficult. When
there are added the difficulties presented by strong coloration
and turbidity, calibration is impossible. Such is the situation to
be faced when dealing with the media and the cultures which
the bacteriologist must handle.

It is sometimes helpful to construct titration curves of a solu-
tion under examination, making measurements after addition of
graded quantities of acid and alkali, in one case with the hydrogen
electrode and in the other case with indicators, preferably indi-
cators of different types. The indicator readings may then reveal
breaks not to be expected from the hydrogen ion relations of the
solution. If, however, no comparison is made with hydrogen
electrode measurements, the observer must rely to a considerable
extent upon his judgment. "Protein errors" are generally the
larger the more complex and concentrated the protein and tend
to decrease with increase in the extent of protein hydrolysis.

There seems to be no way then to deal with either the protein
or the salt error of indicators but to rely upon the use of those
indicators which give relatively small errors, to keep in mind the
order of magnitude of the error to be expected from the general
nature of the solution tested, and, in important cases, to standard-
ize to the electrometric basis as an arbitrary provisional standard.

Because of the great variety of solutions tested by the colori-
metric method it is impracticable to give a condensed statement
of the probable errors. Elaborate tables of colorimetric and
electrometric comparisons are given by S0rensen (1909) for the

ERRORS IN COLORIMETRIC DETERMINATIONS 123

cases he studied. Clark and Lubs (1917) have tabulated their
results with the sulphonphthalein indicators.

In the work of Michaelis or that of Kolthoff salt corrections
are for the most part established by means of hydrogen electrode
measurements. Wells (1920) has tabulated some data for cresol
red in a manner useful for a certain type of water study (cf. Mc-
Clendon 1917), and Brightman, Meacham and Acree (1920) have
recorded the effects of different concentrations of phosphate
buffer.

The "protein error" and the "salt error" have been given
prominence in the literature partly because both have to be taken
into consideration in dealing with biological solutions, and partly
because there is to be perceived underlying the salt error a most
interesting phenomenon of rather general interest. However,
this emphasis should not obscure the fact that there are specific
conditions for each indicator which render that indicator useless
for the determination of pH. For instance alizarine, in passing
from the phosphate to the borate buffer mixtures exhibits a sudden
transition which has all the appearances of a specific effect of the
borate upon the indicator. And alizarine is not alone in this
peculiarity. This same alizarine in the presence of aluminium
may form a lake and with proper pH control may be made a use-
ful reagent for aluminium in place of a very poor acid-base indica-
tor. Zoller (1921) has called attention to the incompatibility
between certain dyes and the phthalate buffers. Many indica-
tors are easily reduced or like methyl red easily reduced and then
so altered that the reduction is irreversible. A number of indi-
cators undergo their color changes slowly or else fade and are
lost to the observer. Other indicators precipitate with certain
cations, for instance Orange IV and Congo with alkali earths.
In short all possibilities must be watched lest the investigator,
venturing upon the study of some new solution, be misled by the
mark of reliability placed upon an indicator tried under limited
circumstances.

Wherever possible it is good practice to test doubtful cases
with two indicators of widely different chemical composition.

As to the effect of temperature variation, comparatively little
work has been done. Gillespie and others have some notes on
the subject and more recently Michaelis and his coworkers have

124

THE DETERMINATION OF HYDROGEN IONS

included temperature data in stating the constants used in the
Michaelis and Gyemant method (see Chapter VIII). Kolthoff
(1921) has extended the theory of School in which account is
taken of the acidic or basic nature of an indicator, but there often
remains some question as to how a given indicator is to be classi-
fied. Kolthoff using the values of Kohlrausch and Heydweiller
for the dissociation constant of water at various temperatures
has reduced his observations to the following table. In this

TABLE 34
Displacement of indicator exponent between 18°C. and 70°C. after Kolthoff

INDICATOR

Nitramine

Phenol phthalein

Thymol blue, alkaline range

a-naphthol phthalein

Curcumine

Phenol red

Neutral red

Brom cresol purple.

Azolitmin

Methyl red

Lacmoid

p-nitro phenol

Methyl orange

Butter yellow

Bromphenol blue

Tropaeolin 00

Thymol blue, acid range . .

pH DIS-
PLACEMENT

-1.45
-0.9 to 0.4
-0.4
-0.4
-0.4
-0.3
-0.7

0.0

0.0
-0.2
-0.4
-0.5
-0.3
-0.18

0.0
-0.45

0.0

pOH DISPLACE-
MENT

0.0
-0.55 to 1.05
-1.05
-1.05
-1.05
-1.15
-0.75
-1.45
-1.45
-1.25
-1.05
-0.95
-1.15
-1.17
-1.45
-1.0
-1.45

RATIO OF
DISSOCIATION
CONSTANT AT

70°C. TO THAT
AT ORDINARY

TEMPERATURE

1.0
About 5
2.5
2.5
2.5
2.0

1.0
1.0

2.5

3.2
14.0
15.0

1.0
10.0

1.0

table the displacement of —0.4 for thymol blue means that if
thymol blue in a solution at 70°C. shows the same color as the
same concentration of this indicator in a buffer of pH 9.4 at
ordinary temperature then the pH of the solution at 70°C. is 9.0.
Corrections for temperatures between room temperature and
70CC. may be interpolated from the data in the table.

ERRORS IN COLORIMETRIC DETERMINATIONS 125

REFERENCES

Abegg-Bose (1899), Arrhenius (1899), Bjerrum (1914), Brightman-Meacham
Acree (1920), Chow (1920), Clark-Lubs (1917), Dawson-Powis (1913),
Gillespie-Wise (1918), Harned (1915), Kolthoff (1916, 1918, 1922),
Lewis (1912), McBain-Coleman (1914), McBain-Salmon (1920),
Michaelis (1920-21), Michaelis-Gyemant (1920), Michaelis-Kruger
(1921), Michaelis-Rand (1909), Palmaer-Melander (1915), Poma
(1914), Poma-Patroni (1914), Prideaux (1917), Rosenstein (1912),
Sackur (1901), SpTensen (1909), S0rensen-Palitzsch (1910), (1913),
Wells (1920), Zoller (1921).
See also Chapter II and page 341.

CHAPTER VIII
Approximate Determinations with Indicators

If you can measure that of which you speak, and can express it by
a number, you know something of your subject; but if you cannot
measure it, your knowledge is meagre and unsatisfactory. — Lord
Kelvin

The distinctive advantages of the indicator method are the
ease and the rapidity with which the approximate hydrogen ion
concentration of a solution may be measured. The introduction
of improved indicators, the charting of their pH ranges, better
definition of degree in "acidity" or "alkalinity," and the illumina-
tion of the theory of acid-base equilibria have developed among
scientific men in general an appreciation of how indefinite were
those old, favorite terms — "slightly acid," "distinctly alkaline,"
and "neutral." There is now a clear recognition of the distinct
difference between quantity and intensity o'f acidity; and for
each aspect there may be given numerical values admitting
no misunderstanding.

Furthermore the clarification of the subject has brought a
perspective which may show where accuracy is unnecessary and
where fair approximation is desirable. In such a case the investi-
gator turns to the indicator method knowing that even if his
results are rough they can still be expressed in numerical values
having a definite meaning to others.

Now a very good approximation may be attained by color
memory and without the aid of the standard buffer solutions
or of the systems presently to be described in which the standard
buffer solutions are dispensed with.

To establish a color memory as well as to refresh it a set of
"permanent" standards is convenient. These may be prepared
with the standard buffer solutions in the ordinary way, protected
against mold growth by means of a drop of toluol, and sealed
by drawing off the test tubes in a flame or by corking with the
cork protected by tinfoil or paraffme. For exhibition purposes
long homeopathic vials make a very good and uniform container.
They may be filled almost to the brim and a cork inserted, if a

126

APPROXIMATE INDICATOR METHODS 127

slit is made for the escape of excess air and liquid. The slit may
then be sealed with paraffine. A hook of spring-brass snapped
about the neck makes a support by which the vial may be fastened
to an exhibition board. A neater container is the so-called typhoid-
vaccine ampoule which is easily sealed in the flame.

If one of a series of standards so prepared should alter, the
change can generally be detected by the solution falling out of
the proper slope of color gradation. But if all in a series should
change, it may be necessary to Gompare the old with new stand-
ards. Because such changes do occur, "permanent" standards
are to be used with caution. The sulfon phthalein indicators
make fairly permanent standards but the methyl red which is an
important member of the series of indicators recommended by
Clark and Lubs (1917) often deteriorates within a short time.

A device which furnishes a color standard to be interpreted by
means of a dissociation curve is the color wedge of Bjerrum (1914).
This is a long rectangular box with glass sides and a diagonal glass
partition which divides the interior into two equal wedges. One
compartment contains a solution of the indicator fully transformed
into its alkaline form, the other a like concentration of the indi-
cator transformed to the acid form. A view through these wedges
should imitate the view of a like depth and concentration of the
indicator transformed to that degree which is represented by the
ratio of wedge thicknesses at the point under observation.
Compare Barnett and Barnett (1920) and Myers (1922).

As an aid to memory the dissociation curves of the indicators
are helpful even when used alone. The color chart shown in
Chapter III is a still better aid to memory and within the limita-
tions mentioned the colors may be used as rough standards.

Sonden (1921) has used colored glasses and Kolthoff (1922)
inorganic salt solutions as color standards.

Colorimetric determination of hydrogen ion concentration without
the use of standard buffer solutions

We have already seen that if an indicator is an acid, its degree
of dissociation, a, is related to the hydrogen ion concentration
of the solution by the equation

[H+] = Ka 1-^^

128 THE DETERMINATION OF HYDROGEN IONS

We have also seen that if Ka, the true dissociation constant
is replaced by the so-called apparent dissociation constant, KiA,
which is a function of Ka and of the constants of tautomeric
equilibria, then a represents the degree of color transformation.
We then have

[H+] = KIA^— ^

or the more convenient form

pH = log — - + log

K " °1

where a may now be considered as to the degree of color trans-
formation. If, for instance, an indicator conducts itself as a simple
acid with apparent dissociation constant 1 X 10~6, we can con-
struct the dissociation curve with its central point of inflection at
pH 6, and then, assuming that this curve represents the relation
of the percentage color transformation to pH, we can determine
the pH of a solution if we can determine the percentage color
transformation which this indicator displays in a tested solution.
Proceeding on these simple and often unjustified assumptions
we can now devise a very simple way of detecting the percentage
color transformation. The following is quoted from Gillespie
(1920) :

We may assume that light is absorbed independently by the two forms
of the indicator, and hence that the absorption, and in consequence of this
the residual color emerging, will be the same whether the two forms are
present together in the same solution or whether the forms are separated
for convenience in two different vessels and the light passes through one
vessel after the other. Therefore, if we know what these percentages are
for a given indicator in a given buffer mixture, we can imitate the color
shown in the buffer mixture by dividing the indicator in the proper pro-
portion between two vessels, and putting part of it into the acid form with
excess of acid, the rest into the alkaline form with excess of alkali.

Gillespie sets up in the comparator (see page 70) two tubes,
one of which contains, for example, three drops of a given indicator
fully transformed into the acid color, and the other of which con-
tains seven drops of the indicator fully transformed into the alka-
line form. The drop ratio 3 : 7 should correspond to the ratio of
the concentrations of acid and alkaline forms of ten drops of the

APPROXIMATE INDICATOR METHODS 129

indicator in a solution of that pH which is shown by the disso-
ciation curve of the indicator to induce a seventy per cent trans-
formation. If then the two comparison tubes and the tested
solution are kept at the same volume, and the view is through
equal depths of each, a matching of colors should occur between
the virage of the two superposed comparison tubes and that of
the tested solution.

Barnett and Chapman (1918) applied this method with
one indicator phenol red but without using the dissociation
curve. Gillespie (1920) extended the procedure to several other
indicators and made use of the dissociation curves so that he
was able to smooth out to more probable values the experimental
data relating drop ratios to pH. This is important because
the experimental error in judging color is not inconsiderable
and if the purely empirical data be made the sole basic standardi-
zation of the method there may be involved a systematic error,
which, added to the error of the individual measurement may
make the cumulative error unnecessarily large. That this had
already occurred was indicated by Gillespie's comparison of
the values for the drop ratios of phenol red given by Barnett and
Chapman on the one hand and the report of the bacteriologists'
committee (Conn, et al., 1919) on the other hand.

Gillespie found the correspondence between the experimental
and the theoretical results predicted on the basis of the simpli-
fying assumptions mentioned above to be very good for the sul-
fon phthaleins, doubtless because of the reasons mentioned in
Chapter IV. He also showed good correspondence in the case
of methyl red but reiterates the fact that phenol phthalein cannot
be treated by means of the simple dissociation curve for a mono
acidic acid, as was mentioned in Chapter IV.

In table 35 are given the pH values corresponding to various
drop ratios of seven indicators as determined by Gillespie. At
the bottom of the table are shown the quantities of acid used to
obtain the acid color in each case. The use of acid phosphate in-
stead of hydrochloric acid in two cases is because the stronger
acid might . transform the indicator into that red form which
occurs with all the sulfon phthalein indicators at very high acidi-
ties. The 0.05 M HC1 is prepared with sufficient accuracy by
diluting 1 cc. concentrated hydrochloric acid (specific gravity 1.19)
to 240 cc.

130

THE DETERMINATION OF HYDROGEN IONS

The alkaline form of the indicator is obtained in each case
with a drop of alkali (two drops in the case of thymol blue).
The alkali solution used for this purpose may be prepared
with sufficient accuracy by making up a 0.2 per cent solution
with ordinary stick NaOH. The indicator solutions may be
made up as described on page 81 . Gillespie prefers the alcoholic
solution in the case of methyl red and specifies it for soil work.

TABLE 35
Gillespie's table of pH values corresponding to various drop-ratios

DROP-RATIO

BROM-

PHBNOL
BLUE

METHYL
RED

BROM-
CRESOL
PURPLE

BROM--

THYMOL

BLUE

PHENOL
RED

CRESOL RED

THYMOL
BLUE

1:9

3.1

4.05'

5.3

6.15

6.75

7.15

7.85

1.5:8.5

3.3

4.25

5.5

6.35

6.95

7.35

8.05

2:8

3.5

4.4

5.7

6.5

7.1

7.5

8.2

3:7

3.7

4.6

5.9

6.7

7.3

7.7

8.4

4:6

3.9

4.8

6.1

6.9

7.5

7.9

8.6

5:5

4.1

5.0

6.3

7.1

7.7

8.1

8.8

6:4

4.3

5.2

6.5

7.3

7 9

8.3

9.0

7:3

4.5

5.4

6.7

7.5

8.1

8.5

9.2

8:2

4.7

5.6

6.9

7.7

8.3

8.7

9.4

8.5:1.5

4.8

5.75

7.0

7.85

8.45

8.85

9.55

9:1

5.0

5.95

7.2

8.05

8.65

9.05

9.75

Produce
acid color <
with

1 cc. of

0.05m

HC1

1 drop

0.05m

HC1

1 drop

0.05m

HC1

1 drop

0.05m

HC1

1 drop

of
0.05m
HC1

1 drop of

2 per cent
H2KP04

1 drop of

2 per cent
H2KPO4

Gillespie proceeds as follows:

Test tubes 1.5 cm. external diameter and 15 cm. long are suitable for
the comparator and for the strengths given for the indicator solutions. It
is advisable to select from a stock of tubes a sufficient number of uniform
tubes by running into each 10 cc. water and retaining those which are filled
nearly to the same height. A variation of 3 to 4 mm. in a height of 8 cm.
is permissible. Test tubes without flanges are preferable. The tubes may
be held together in pairs by means of one rubber band per pair, which is
wound about the tubes in the form of two figure 8's.

It is convenient to use metal test tube racks, one for each indicator,
each rack holding two rows of tubes, accommodating one tube of each pair
in front and one in back. For any desired indicator a set of color standards
is prepared by placing from 1 to 9 drops of the indicator solution in the 9
front tubes of the pairs and from 9 to 1 drops in the back row of tubes. A

APPROXIMATE INDICATOR METHODS 131

drop of alkali is then added to each of the tubes in the front row (2 drops in
the case of thymol blue), sufficient to develop the full alkaline color and
a quantity of acid is added to each of the tubes in the back row to develop
the full acid color without causing a secondary change of color (see table

35 for quantities) The volume is at once made up in all

the tubes to a constant height (within about one drop) with distilled water,
the height corresponding to 5 cc.

These pairs are used in the comparator and matched with the
tested solution. This tested solution is added to ten drops of the
proper indicator until a volume of 5 cc. is attained and the tube
is then placed in the comparator backed by a water blank.

Gillespie describes the use of the comparator (page 70) and a
modification for the accommodation of sets of three tubes used
when colored solutions have to be compared. He also discusses
a number of minor points and cautions against the indiscriminate
comparison of measurements taken at different temperatures.
For the details the original papers should be consulted. Were
it not that the writer has seen evidence that the method has been
applied with neglect of volume or concentration relations called
for by the theory involved and carefully specified by Gillespie,
it would seem unnecessary to advise that the principles be under-
stood before the method is used. Certain other misconceptions
of theory and practice found in a treatment of the method by
Medalia (1920) have been corrected by Gillespie (1921).

A very judicious appraisal of the method's value was given by
Gillespie in these words:

The method should be of especial use in orienting experiments, or in
occasional experiments involving hydrogen ion exponent measurements,
either where it is unnecessary to push to the highest degree of precision
obtainable, or where the investigator may be content to carry out his
measurements to his limit of precision and to record his results in such a
form that they may be more closely interpreted when a more precise study
of indicators shall have been completed.

For the elaboration of certain manipulative details see Van
Alstine (1920).

If an indicator has only one color, for instance if it is yellow
in the alkaline form and colorless in the acid form, it is evident
that the method employed by Gillespie may be used with the
slimination of one of the sets of tubes. Thus if 10 cc. of a tested

132

THE DETERMINATION OF HYDROGEN IONS

solution containing 1 cc. of para nitro phenol matches 10 cc. of
an alkaline solution containing 0.2 cc. of the same solution of
the same indicator, it is known that the tested solution has in-
duced a 20 per cent transformation of the indicator. Then a
is 0.2. If now KIA has been determined, and if it has been shown
that the simple dissociation formula holds for the indicator in
use, equation 10 may be solved for pH.

This procedure has been developed by Michaelis and co-
workers; Biochem. Z. (1920) 109, 165; Biochem. Z. (1921) 119,
307; Deut. med. Wochenschr. (1920) 46, 1238; 47, 465, 673;
Z. Nahr. Genussm. (1921) 42, 75; Z. Immunitatsf. (1921) 32,
194; Wochenschrift Brau. (1921) 38, 107. Calculations are

aided by the use of a table relating a to log - . Such a

1 — a

table, somewhat more elaborate than that required for this special
purpose, will be found on page 460 of the appendix.

It is obviously necessary that KIA shall have been determined
or that the actual experimental data relating the degree of color
transformation to pH along the "dissociation curve" shall have
been obtained. This necessary, fundamental "calibration"
has been worked out by Michaelis and Gyemant (1920) and
Michaelis and Kriiger (1921) (using hydrogen electrode measure-
ments as a basis) for a series of one-color indicators. In the fol-
lowing table are the pH values of the half -transformation points
of the indicators used by Michaelis and Gyemant. These points

correspond to log =r~ (see p. 26).

-"■TA

TABLE 36
pH values of the half-transformation points of indicators. After Michaelis

2, 6 dinitro phenol. . .
2, 4 dinitro phenol. . .

p-nitro phenol

m-nitro phenol

Phenolphthalein

Alizarine Yellow GG

TEMPERATURE

10°

20°

30°

40°

3.74

3.68

3.62

3.56

4.11

4.05

3.99

3.93

7.27

7.16

7.04

6.93

8.43

8.32

8.21

8.09

9.82

9.70

9.58

9.46

11.26

11.13

11.00

10.87

50°

3.51
3.85
6.81
7.99
9.34
10.74

APPROXIMATE INDICATOR METHODS

133

Now phenolphthalein, as we have already mentioned, is poly-
acidic with dissociation constants so close to one another that
the simple equation of a mono acid cannot be used. Alizarine
Yellow GG suffers the same disadvantage. Consequently it is
necessary in these cases to abandon the simple equation and the
dissociation constants given above and to tabulate the experi-
mental data. Michaelis and Gyemant have given the following
tabulations.

TABLE 37
Degree of color, a, shown by phenolphthalein at indicated pH values.
Temperature 18°C.

0.01

8.45

0.16

9.10

0.55

9.80

0.014

8.50

0.21

9.20

0.60

9.90

0.030

8.60

0.27

9.30

0.65

10.00

0.047

8.70

0.34

9.40

0.70

10.10

0.069

8.80

0.40

9.50

0.75

10.20

0.090

8.90

0.45

9.60

0.80

10.30

0.120

9.00

0.50

9.70

0.845
0.873

10.40
10.50

TABLE 38
Degree of color, a, shown by alizarine yellow GG at indicated pH values.

Temperature 20°C.

0.13

10.00

0.56

11.20

0.16

10.20

0.66

11.40

0.22

10.40

0.75

11.60

0.29

10.60

0.83

11.80

0.36

10.80

0.88

12.00

0.46

11.00

For 2, 5-dinitrophenol log

is 5.15 for solutions of very

low salt concentrations, 5.08 for solutions of 0.15 M salt concen-
tration and 5.02 for solutions of 0.5 M salt concentration.

For 3, 4-dinitro phenol log ~zz~ is about 5.3 and for 2, 3-dini-

-"■IA

trophenol about 4.8.

134 THE DETERMINATION OF HYDROGEN IONS

With these data we are now prepared to measure pH values
without the use of standard buffer solutions.
The following indicator solutions are used:

1. 2, 4 dinitro phenol (a dinitro phenol) 0.05 per cent aqueous solution

2. 2, 6 dinitro phenol (/3 dinitro phenol) saturated aqueous solution

formed at high temperature and filtered from crystals.

3. 2, 5 dinitro phenol (y dinitro phenol) 0.025 per cent- aqueous

solution.

4. 3, 4 dinitro phenol (5 dinitro phenol) concentration not given.

5. 2, 3 dinitro phenol (e dinitro phenol) concentration not given.

6. p-nitro phenol 0.1 per cent aqueous solution.

7. m-nitro phenol 0.3 per cent aqueous solution.

8. phenol phthalein 0.04 per cent solution in 30 per cent alcohol.

9. Alizarine yellow GG (salicyl yellow, m-nitrobenzene azo salicylic

acid) saturated alcoholic solution diluted to convenient strength.

Test tubes must be of equal bore. A measured amount of the
solution to be tested (e.g. 10 cc.) is mixed with the proper indicator
in such amount that a rather weak color is developed. To a
second test tube containing 9 cc. N/100 NaOH there is added
such a volume of the indicator solution that the color developed
approximately matches that of the first tube. The volume of
the second tube is now made up to the volume of the first. If the
two tubes do not match in color, another trial is made with more
or less indicator until a color match is obtained. The amount
of fully transformed indicator in the second tube then corresponds
to that amount of indicator in the first tube which has been trans-
formed to the colored tautomer. Let us assume that 1.0 cc.
was added to the tested solution and that a color match occurs
when 0.1 cc. of the same indicator solution was placed in the second
alkaline tube and made up to the volume of the first. Then the
percentage color transformation induced by the tested solution

was 10.

Hence a = 0.1 and log = — 0.95.

1 — a

If the indicator used was p-nitrophenol and the temperature
was 20°C. pH = 7.16 - .95 = 6.21 (6.2)

If the indicator was phenolphthalein table 37 shows that the
pH was about 9.0.

For routine work in the range pH 2.8 to 8.4 Michaelis (1921)
recommends the following system.

APPROXIMATE INDICATOR METHODS

135

To uniform test tubes are added seriatim the volumes of indica-
tor solution given in the following tables, the indicator solution
being prepared by diluting the stock solutions (page 134) ten times
with 0.1 normal soda solution (sic). Each tube is now filled to a
7 cc. mark with the soda (sic) solution. (In the original paper
Michaelis and Gyemant describe dilutions with N/100 NaOH
solution.)

TABLE 39

m-nitro phenol

Tube number

Cubic centimeters of indicator.
pH

1
5.2

8.4

4.2
8.2

3
3.0

8.0

4
2.3

7.8

5
1.5
7.6

6
1.0
7.4

7
0.66
7.2

0.43
7.0

9
0.27
6.8

p-nitro phenol

Tube number

Cubic centimeters of indicator. .
pH

4.05

3.0

2.0

1.4

0.94

0.63

0.4

0.25

7.0

6.8

6.6

6.4

6.2

6.0

5.8

5.6

18
0.16
5.4

#, 5-dinitro phenol (y dinitro phenol)

Tube number

19
6.6

5.4

20
5.5
5.2

21
4.5
5.0

22
3.4

4.8

23
2.4
4.6

24
1.65
4.4

25
1.1

4.2

0.74
4 0

2, 4-dinitro phenol (a dinitro phenol)

Tube number

Cubic centimeters of indicator.
pH

6.7

5.7

4.6

3.4

2.5

1.74

1.20

0.78

4.4

4.2

4.0

3.8

3.6

3.4

3.2

3.0

35
0.51

2.8

The test tubes are sealed with paraffined corks and when not
in use are protected from the light.

To test a solution for its pH value 6 cc. are taken and 1 cc.
indicator solution added. The solution is then compared with
the standards.

For testing the pH values of waters Michaelis (1921) operates
as follows:

A stock solution containing 0.3 gram pure m-nitro phenol in
300 cc. distilled water is diluted before use by adding to 1 cc.
of the stock 9 cc. distilled water. There are used flat bottom
tubes of about 25 cm. height and 14 mm. internal diameter having
such uniformity that 40 cc. of water will stand at a height of

136 THE DETERMINATION OF HYDROGEN IONS

between 22 and 23 cm. To six such tubes are added seriatim
0.25; 0.29; 0.33; 0.38; 0.45 and 0.50 cc. of the diluted m-nitro
phenol solution. To each tube are added 40 cc. of an approximately
N/50 NaOH solution freshly prepared by dilution of an approxi-
mately normal solution. These are the standards.

To test a water, 40 cc. are added to a tube of correct dimensions
and to this is added sufficient indicator to develop a. color within
the range of the standards, preferably near the brighter of the
standards. Comparison is now made as in Nesslerization, after
having waited two minutes for completion of the mixing.

The amount of indicator in the alkaline, matching standard
corresponds to the amount transformed to the colored form by
the tested solution. Therefore, the cubic centimeters of indica-
tor in the standard divided by the cubic centimeters in the tested
solution is a, the degree of color transformation, or when multi-
plied by 100 the percentage color transformation.

Michaelis and his co-workers have tabulated corrections for
temperature and for salt concentrations. The operator should
determine for himself not only the order of accuracy required in
his problem but his own ability to make readings with that pre-
cision which will make corrections significant. He may then
refer to the original papers for tables giving corrections for salt
effects and for temperature. The order of magnitude of these
corrections may be seen in the following example.

For m-nitrophenol Michaelis and Kriiger give the following

values of log zz~ at 17°C. in solutions of the indicated salt
concentrations.

TABLE 40

MOLECULAR 8ALT CONTENT

KAI

O-0.01

8.33

0.05

8.28

0.10 i

8.23

0.15

8.22

0.20

8.18

0.3-0.6

8.17

to 1.0

8.15

APPROXIMATE INDICATOR METHODS

137

The temperature corrections to be added when m-nitrophenol
is used at temperatures other than 17.5°C. are as follows.

TABLE 41

t°

CORRECTION

t°

CORRECTION

+0.10

-0.06

+0.06

-0.11

+0.02

-0.15

17.5

±0.00

-0.18

-0.02

-0.22

-0.26

In spite of the fact that the nitro compounds used by Micha-
elis and Gyemant are of wan color and those tried in the survey
made by Clark and Lubs were neglected for this reason, Micha-
elis and Gyemant describe the application of their method to
colored solutions.

Advantage is taken of the fact that many solutions are inappre-
ciably altered in pH by diluting five or even ten times (see page
37). For dilution, Michaelis and Gyemant use freshly boiled
NaCl solution of a concentration approximately that of the test
solution. If on dilution the natural color still interferes with
the use of an indicator, the natural color may be duplicated in
the standard by the use of supplementary dyes such as S0rensen
uses. Or, if addition of alkali does not alter the natural color of
the solution under test, the, standard may be made up with an
alkaline solution of the tested solution itself. In this case it is
necessary to be on guard against the buffer action and to add
alkali until no increase in the color of the indicator is observed.

Without doubt the preferable procedure to follow when apply-
ing the Michaelis and Gyemant method or any other method to
colored solutions is to use the "comparator" described on page
70 and illustrated in figure 8.

The method of Michaelis and Gyemant is fundamentally the
same as that of Gillespie and should, therefore, be used with the
qualifications which Gillespie has stated. There is a distinct
advantage in the use of the nitro phenols for they have been found
to have relatively small protein and salt errors. It is sometimes
accessary to use very high concentrations of the indicator, and

138 THE DETERMINATION OF HYDROGEN IONS

in such circumstances one must be on guard against the effect of
the indicator itself or of impurities.

Indicator paper. Although a favorite form of indicator is the
deposit on a strip of paper (for example the familiar litmus paper)
it is to be avoided unless the use of an indicator solution is pre-
cluded. It is to be avoided because the factors involved in the
reaction between solution and indicator are made complex by
the capillary action of the paper or the material entrained in
these capillaries. On the other hand there are occasions when
an approximate measure of pH is sufficient and when an indicator-
paper is to be preferred. On such an occasion it is desirable to
know the difficulties to be encountered. We are indebted to
Walpole (1913) and others but particularly to Kolthoff (1919,
1921) for investigations on this subject. Kolthoff has given
particular attention to the sensitivity of indicator papers when
used in titrations, a situation where there is generally but little
buffer action near the end-point. Under such circumstances
there are to be regarded a number of details which are described
at length in Kolthoff' s papers. Several of these details will be
perceived if we describe some of the more important aspects of
the indicator-paper method of determining pH.

In general one must ride either horn of the following dilemma.
The paper is sized, in which case the buffer action of the tested
solution must be strong enough and allowed time enough to over-
come the buffer action of the sizing. Or the paper has the quali-
ties of filter paper, in which case the solution tested will spread
and leave rings of different composition formed by the adsorp-
tive power of the capillaries.

Kolthoff found that various treatments and selections of filter
paper are of secondary importance, so the choice lies between
sized and unsized paper. Now certain coloring matters are ad-
sorbed by filter paper so that a separation is possible and the
clear solution can be found in a ring about the point of contact
between a tested colored solution and the indicator paper. But
beyond this ring is a much more dilute one and unless one knows
the properties of the system under examination it is not easy to
correctly estimate the pH of the solution from the appearances
of the paper.

Although coated paper may lose in sensitivity by not taking

APPROXIMATE INDICATOR METHODS 139

up so much indicator as filter paper and must be used with strongly
buffered solutions it is the more convenient. In any case the
paper should be left in contact with the tested solution a generous
length of time, for the establishment of equilibrium may be very
slow (Walpole), and there must be instinctively exercised a men-
tal plotting of the time curve.

If, after having exhausted all other methods, it is found that
the indicator-paper method is the better adapted to a particular
set of circumstances, the procedure should be calibrated to the
purpose at hand rather than forced to render accurate pH values.

Dilution. As indicated in Chapter II a well buffered solution
may often be moderately diluted without seriously altering the
pH.

When dealing with complex solutions which are mixtures of
very weakly dissociated acids and bases in the presence of their
salts, and especially when the solution is already near neutrality
dilution has a very small effect on pH, so that if we are using the
crude colorimetric method of determining pH a five-fold dilution
of the solution to be tested will not affect the result through the
small change in the actual hydrogen ion concentration. Differ-
ences which may be observed are quite likely to be due to change
in the protein or salt content. For this reason as well as for other
reasons Glark and Lubs (1917) considered it wise to use M/20
standard comparison solutions instead of more concentrated stand-
ards for bacteriological media where dilution is often advantageous.
The salt content of the standards undoubtedly influences the
indicators and should be made as comparable as is convenient
with the salt content of the solutions tested when these are diluted
to obtain a better view of the indicator color.

The conclusion that dilution has little effect on the hydrogen
ion concentrations of many solutions has long been recognized.
Michaelis (1914) found little change in the pH of blood upon
dilution, and Levy, Rowntree, and Marriott (1915) depended
upon this in part in their dialysis method for the colorimetric
determination of the hydrogen ion concentration of blood. Hen-
derson and Palmer (1913) have used the dilution method in de-
termining the pH of urines, and Paul (1914) records some experi-
ments with wines the pH values of which were affected but little
by dilution. The legitimacy of dilution has been tacitly admitted

140 THE DETERMINATION OF HYDROGEN IONS

by bacteriologists in their procedure of diluting media to be
titrated to what is in reality a given pH as indicated by
phenolphthalein.

In the examination of soil extracts colorimetrically little could
be done were the "soil-solution" not diluted. Whatever may be
the effect it is certain that the correlations between the pH values
of such extracts and soil conditions is proving of great value (see
Chapter XXI). Wherry has developed a field kit of the sulfon
phthalein indicators with which he has found some remarkable
correlations between plant distribution and the pH of the native
soils. This field kit is now on the market.

The use of indicators in bacteriology. Perhaps no other science
requires such continuous routine use of indicators as does bac-
teriology. This use is chiefly in the adjustment of the reaction
of culture media and in the testing of the direction and limits of
fermentation. While these are but examples, the frequency with
which they become matters of routine warrant a brief outline of
special procedures.

If experience has shown that the pH of the medium may lie
within a zone about 0.5 units of pH wide, it is sufficient to add
unstandardized acid or alkali, as the case may be, until a portion
of the medium tested with the proper indicator in proper concen-
tration approximately matches that color standard shown in the
color chart of page 50 corresponding to the pH value to be ap-
proximated. This requires experience in overcoming the confusing
effect of the natural color of the medium and also a well established
sense of color memory. The beginner should proceed in some
such way as the following.

It is desired, for instance, to adjust a colorless medium to pH
7.5. The medium as prepared is somewhat below the final vol-
ume. A quick, rough test at room temperature shows that the
pH value lies between 6.0 and 6.5. Therefore, alkali must be
added. The 'alkali solution to be used need not be standardized
but may be about 1 normal. An exact one-in-ten dilution of
this is run into 5 cc. of the medium to which has been added 5
drops of phenol red solution. Titration is continued until the
color nearly matches 10 cc. of standard buffer "7.5." The tube
of medium is now diluted to 10 cc. so that a color comparison
may be made between test solution and standard, each contain-

APPROXIMATE INDICATOR METHODS 141

ing the same concentration of indicator. The tubes are viewed
through equal depths of solution. If the desired point 7.5 has
been overstepped another trial is made. If 7.5 is not reached a
moderate addition of alkali may be made without serious viola-
tion of volume requirements, and a second reading is taken.

Having made estimates of the pH values in the two readings
an interpolation is made of the amount of dilute alkali required
to bring the medium to exactly pH 7.5. From this is calculated
the amount of the stronger alkali required for the main batch.
Having added this a check determination is made. When
finally adjusted the medium is diluted to its final volume. Most
culture media suffer alterations of their pH values during sterili-
zation and consequently allowance must be made if the final
pH value is to be exact. This allowance will vary with the medium
but can easily be determined for a standard medium prepared
under uniform conditions.

When the color or turbidity of a tested solution interferes with
direct color comparisons proceed as above but make comparisons
by means of the Walpole compensation method described on
page 70.

It need hardly be said that if the requirements of an organism
are such that the desired pH value cannot be obtained with phenol
red a more suitable indicator is selected from table 6 and if the
medium requires the addition of acid an unstandardized acid
solution approximately normal (or stronger) and an exact 1:10
dilution of this are substituted for the alkali solutions mentioned
above.

In testing fermentations it often happens that the final hydro*-
gen ion concentration is of more significance than the amount of
acid or alkali formed; but the two distinct types of data are not
to be confused to the complete displacement of either. It is
sometimes convenient to incorporate the indicator with the
medium provided the indicator is not reduced or destroyed by
the bacterial action. The sulfon phthaleins are particularly use-
ful for they are not reduced except by the more active anaerobes.
Brom cresol purple replaces litmus in the common milk-fermenta-
tion tests without introducing that confusion which the reduction
of litmus causes. It reveals differences in pH even beyond the
range of its usefulness for ordinary measurements, passing from a

142 THE DETERMINATION OF HYDROGEN IONS

greyish blue in normal milk to more and more brilliant yellows
with the development of acidity, and to a deep blue with the
development of alkalinity. For further details see Clark and
Lubs (1917).

In the method of Clark and Lubs (1915, 1916) for the differenti-
ation of the two main groups of the coli-aerogenes bacteria, as
well as in the similar method of Avery and Cullen (1919) for
separating streptococci, the composition of the medium is so
adjusted to the metabolic powers of the organisms, that the
reaction is left acid to methyl red in one case, and alkaline in
the other. No exact pH measurements are necessary. In cases
where large numbers of cultures falling within the range of one
indicator are to be tested, the cultures may be treated with the
indicator and compared by grouping. A careful determination
made upon one member of a homogeneous group will serve for all.
In this way large numbers of cultures may be tested in a day.

Special uses. While on the subject of approximate determina-
tions with indicators a word may be said about the usefulness of
the quick, rough test.

Almost every investigator has come to realize that among the
mistakes in labeling chemicals the more frequent are cases in
which a basic salt is labeled as an acid salt and vice versa. Now
a solution of NajjHPC^, for example, has a pH value, which,
while easily displaced (see figure 5), distinguishes it definitely
from a solution of NaH2P04 or Na3P04. Indeed some idea may
be obtained of the degree of impurity if the pH value of a dilute
solution is displaced definitely from about pH 8.5. Some serious
accidents are said to have occurred in medical practice by the
use of sodium citrate purported to be neutral and too late found
to be acidic. One short, swift test with an indicator could have
revealed the situation, and averted the accident.

Indeed there are a great many substances solutions of which
have either a buffered and definite pH value, as in the case of
acid potassium phthalate, or else a pH value easily displaced
by impurities from that of the absolutely pure substance but
still falling within limits, as in the case of the primary and second-
ary phosphates. When properly defined, such values can be
made part of the specifications for purity. Especially in the
case of drugs which are often used beyond the reach of the assay

APPROXIMATE INDICATOR METHODS 143

laboratory a simple indicator test should prove helpful as sug-
gested by Evers (1921) and especially emphasized by Kolthoff
(1921).

In the case of milk it is quite impossible to define the pH by a
comparison of the color of an indicator in the milk with the
color of the indicator in a clear standard; yet differences are made
distinctly evident, and, if taken only for what they actually
mean, are helpful in the grading of milk and in the study of the
conduct of different bacteria inoculated into sterile milk. Clark
and Lubs (1917) called attention to the superiority of the sul-
fonphthalein indicators, especially brom cresol purple, for this
purpose.

Spotting. When only small quantities of solution are available or
when highly colored solutions are to be roughly measured, their ex-
amination in drops against a brilliant white background of "opal"
glass is often helpful. In the examination of colorless solutions
comparisons with standards may be made as follows. A drop of
the solution under examination is mixed with a drop of the proper
indicator solution upon a piece of opal glass. About this are
placed drops of standard solutions and with each is mixed a
drop of the indicator solution used with the solution under
examination. Direct comparison is then made. Felton who
developed details in this method for the examination of small
quantities of solutions used in tissue-culture investigations found
mixtures of indicators of particular value for orientation. Equal
parts of methyl red and brom thymol blue, for instance, give
brilliant color contrasts in this drop method between about pH
4.6 and 7.6; but with an unsatisfactory zone between 5.6 and 6.2.
Methyl red and brom cresol purple are used between pH 4.6
and 7 while for rough work between 1.2 and 9 methyl red and
thymol blue are used. These mixtures are used only as "feel-
ers." The opal glass or porcelain upon which the tests are to be
made should be carefully tested for the absence of material
seriously affecting the acid-base equilibria of the material under
examination. Errors due to unequal drops, evaporation and
impurity of indicator are to be watched for. For further details
see Felton (1921).

CHAPTER IX

Outline of the Electrometric Method

A noble metal coated with platinum black, which will hold large
quantities of hydrogen, may be made to serve as a hydrogen elec-
trode. When it is laden with hydrogen and immersed in a solution
containing hydrogen ions, there is exhibited a difference of elec-
trical potential between solution and electrode which is depend-
ent upon the concentration of the hydrogen ions; just as the
potential difference between a silver electrode and a solution of
silver ions is dependent upon the concentration of the silver ions.

We have no reliable means of measuring this single potential
difference; but when we join two hydrogen electrodes, as shown
in figure 13, we can not only measure the difference between the
aforementioned differences of potential, i.e., the total electro-
motive force (E. M. F.) of the "gas chain" as it is called, but we
can also derive an equation showing how this E. M. F. will vary
with the ratio of the concentrations of the hydrogen ions about
the two electrodes. If C is the concentration of the hydrogen ions
in one solution and C the concentration in the other, the E. M. F.
of the combination will be related to the ratio of the concentrations
by the following equation expressed in numerical form for a
temperature of 25°C.

E. M. F. = 0.059 log §-
C

We shall leave to the next chapter the derivation of the equa-
tion and shall now put it in a form not restricted to the particular
temperature of 25°C. assumed above.

C
E. M. F. = 0.000,198,37 T log ~;

Here T is the absolute temperature, the zero point of which is
273.09° below 0°C. A table giving the values of 0.000,198,37 T
for various temperatures centigrade is given in the Appendix.
Thus if we join two hydrogen electrodes as illustrated in figure
13 measurements of the electromotive force of the chain and of

144

OUTLINE OF ELECTROMETRIC METHOD

145

the temperature allow us to calculate the ratio of the one hydro-
gen ion concentration to the other. Then if one hydrogen ion
concentration is known we may derive the other.

As the "known" there may be used any one of the buffer solu-
tions described in Chapter VI. The reader should note, however,
that the values of these "known" solutions are derived from

e:->-3£

- - - -o-

n't".'. *

SSL,

ihsos

= -=ur=^o^

Fig. 13. Diagram op Concentration Chain of Hydrogen Electrodes

hydrogen electrode measurements which, as we have just seen,
furnish ratios only. Some ultimate standard is therefore implied.
This is discussed in Chapter XIX.

If there be no means at hand for measuring the electromotive
force but there is available a galvanometer or a home-made capil-
lary electrometer for detecting small currents, the following
procedure may be used. Two hydrogen electrodes are set up as
in figure 13. By means of the buffer solutions described in Chap-
ter VI the hydrogen ion concentration in one electrode vessel is
varied until no difference of potential occurs between the two
electrodes. This point is determined by absence of deflection

146 THE DETERMINATION OF HYDROGEN IONS

in the galvanometer or by no change in the meniscus of the capil-
lary electrometer. Then C = C in the above equation.

Instead of setting up two hydrogen electrodes, one of which
is a known standard, it is generally more convenient to replace
the standard hydrogen electrode by a more permanent "half
cell" such as the "calomel electrode." This is an electrode of
mercury covered with calomel in the presence of a definite KC1
solution, for example saturated KC1 solution. If this so-called
"saturated calomel electrode" is used, a tube containing sat-
urated KC1 is led directly to the solution in the hydrogen electrode
vessel.

Now suppose that in the first place there were used two hydro-
gen electrodes as in figure 13, and let it be assumed that one of
these was immersed in a solution normal with respect to hydro-
gen ions. Let C be identified as 1 normal and C, the unknown

1
be less than 1 normal. Then E. M. F. = 0.000,198,37 T log 7J

Now suppose that the normal hydrogen electrode is connected
with a "saturated calomel electrode." We might then have
an arrangement as follows:

(saturated calomel electrode

II
III

►normal hydrogen electrode
(hydrogen electrode in [H+] = C'

Suppose the difference II has already been determined and
that I is measured in the immediate experiment. Then I —
II = III. Having found III, we can use the equation for two
hydrogen electrodes, one of which is the "normal," and so solve
directly for C

At 25°C. the mercury of the calomel electrode is 0.246 volt
more positive than the platinum of the normal hydrogen elec-
trode.

Hence: observed E. M. F. - 0.246 = III

I - II = III

III = 0.000,198,37 T log pp.

At 25°C, T = 273.09 + 25 = 298.09.

OUTLINE OF ELECTROMETRIC METHOD 147

Then observed E. M. F. - 0.246 = 0.0591 log —,.

But log — ; = pH.

Observed E.M.F. - 0.246 „

= pH.

0.0591 F

If the observed E. M. F. is 0.648, pH = 6.80.

Although it is impracticable to describe at this point the details
of a complete system for the measurement of hydrogen ion con-
centration an outline may be given with which to coordinate
the main features as they will develop in subsequent chapters.

Figure 14 illustrates a simple system which may be put together
from inexpensive material. It is not a system which can be
recommended for precise or even routine measurements, but it
will work and is well adapted to show the principles concerned.

Hydrogen, prepared by one of the methods described in Chap-
ter XV, passes into the hydrogen electrode vessel A and escapes •
at B. Connected with this vessel by the siphon S, filled with a
saturated KC1 solution, is the calomel electrode M consisting of a
layer of mercury covered by calomel under a saturated solution
of KC1. The hydrogen electrode H consists of a piece of plati-
num foil covered with platinum black. It is welded to a plati-
num wire which is sealed into the glass tube.

Hydrogen is bubbled through the solution in A until solution
and electrode are thoroughly saturated with the gas.

The difference between the potential difference at the mercury-
calomel junction and the potential difference at the hydrogen
3lectrode-solution junction is now measured by means of a po-
tentiometer. A simple form of this is illustrated.

A storage battery P sends current through the rheostat R, the
calibrated resistance-wire K-L and the fixed resistance L-F. By
properly setting the switch O a Weston cell W having an electro-
notive force of 1.018 volts can be connected to K and F, the
f pole of the Weston cell being connected to the + side of the
>attery current. The rheostat R is now varied until there is
io deflection of the galvanometer or electrometer E. Then the
i lifference of potential between K and F is equal to the E. M. F.
t f the Weston cell. The resistance K-L is such that when the

148 THE DETERMINATION OF HYDROGEN IONS

above adjustment is made the difference of potential between
K and L is one volt. A scale properly divided is placed beside
the wire K-L. When the sliding contact X is at K there will be
no difference of potential between X and K. When X is at L
the difference of potential between X and K will be one volt.
When X is at some intermediate position the difference of potential
between X and K will be that fraction of one volt indicated by
the scale.

Having first carefully adjusted the potentiometer by means
of the standard Weston cell the switch O is thrown to connect
the calomel electrode-hydrogen electrode system and X is slid
in one direction or the other until the galvanometer E shows no
deflection. Then the difference of potential between X and
K is equal to the difference of potential between mercury and
platinum.

The temperature is read and the data put into the equations
given above.

Neither measured E. M. F. nor Weston cell should be left in
circuit for more than an instant. While switch 0 can be used
for this momentary completion of circuit, it is more convenient
to use a telegraph key in the galvanometer circuit.

If care be taken to maintain the hydrogen at barometric pres-
sure, the effects of minor variations of the barometer from sea
level conditions and of displacement of hydrogen by water vapor
may be neglected in rough measurements. A discussion of the
barometric pressure is found in the next chapter.

In all cases where two unlike solutions are joined as in figure
13, there will develop a local potential difference at the liquid
junction. To deal with this precisely is the most difficult of the
problems encountered. The subject is discussed in Chapter XI.
In very many instances, however, the employment of a saturated
solution of KC1 as is specified in the apparatus illustrated in
figure 14, reduces the liquid junction potential difference to an
order of magnitude which is negligible.

Since variations may occur in the calomel electrode or in the
reliability of the hydrogen electrode it is well to check the system
frequently by means of measurements made with standard solu-
tions. Some of these are described in Chapter XVIII.

In the use of the potentiometer the elementary principles
must be understood lest standard cells or half-cells be injured

OUTLINE OF ELECTROMETRIC METHOD

149

or quite erroneous results obtained. Therefore, these principles
are discussed in Chapter XIV.

Fig. 14. A Simple Arrangement for Electrometric Measurement

of pH.

Were it not for the fact that several experimenters have tried
to make hydrogen electrode measurements by use of conductivity
nstruments, it would seem hardly necessary to say that the meas-
lrement of conductivity or its reciprocal, resistance, is a proce-
lure entirely different from the measurement of electromotive
orces or potential differences.1

1 The surprising number of cases in which this confusion has been
evealed may be an interesting psychological result of the emphasis hitherto
)laced upon conductivity measurements, sometimes to the entire exclusion
if any reference to potentiometric measurements.

150 THE DETERMINATION OF HYDROGEN IONS

If the beginner is puzzled by the array of apparatus described
in the following pages he may welcome the following suggestion.
The main outline of a problem can often be denned by the use
of the Hildebrand electrode used in connection with the saturated
calomel half-cell and by using as a potentiometer the voltmeter
system. This set of apparatus is illustrated in figure 28. It not
infrequently happens that the outlining of a problem with this or
a comparable system will indicate that further refinement would
be useless or confusing. It also frequently happens that the errors
suggest phantom relations or obscure existing relations of im-
portance. It is, therefore, advisable whenever possible to keep
the accuracy of measurements just ahead of the immediate de-
mands. To meet this requirement the investigator must gain
the ability to judge for himself the apparatus required and it is
to contribute toward this and the pleasure of work that the follow-
ing chapters are written in some detail. If the reader does not
care to work out the peculiar requirements of his problem he is
advised, after having outlined his problem with the system men-
tioned above, to obtain a reliable potentiometer of standard,
not unique, design and to use the system illustrated in figure 19.
In the first instance accurate temperature control is unnecessary.
In the second instance it is advisable if for no other purpose than
the avoidance of vexatious uncertainties.

CHAPTER X

Theory of the Hydrogen Electrode

In treating the theory of the hydrogen electrode we shall first
consider Nernst's (1889) conception of electrolytic solution tension
as a useful way of remembering certain important relations and
then pass to the thermodynamic derivation of the E. M. F. of
a concentration cell.

If a metal be placed in a solution of its salt there will be a differ-
ence of electrical potential between metal and solution which will
vary in an orderly manner with the concentration of the metal ions.
To account for the difference of potential Nernst assumed that a
metal possesses a characteristic solution tension comparable with
the vapor pressure of a liquid, or, better, with the solution pres-
sure of a crystal of sugar — but with the important qualification
that it is the metal ions which pass into solution. Imagine first
that the metal is in contact with pure water. The metal ions
passing into solution carry their positive charges and leave the
metal negative. Thus there is established a so-called double
layer of electrical charges at the interface between metal and solu-
tion, the solution being positively and the metal negatively
charged relative to one another. This potential difference forcibly
opposes further dissolution of metallic ions, for the relative posi-
tive electrical field in the solution and the relative negative field
in the metal restrain any further migration of positively charged
Dodies from the metal to the solution. Equilibrium is established
vhen the electrostatic control equalizes the solution pressure.
If now there are already in the solution ions of the .metal, the
•elative electrostatic field in the solution has already been par-
ially established, fewer ions will escape from the metal and the
netal is left more positive.

Therefore the higher the concentration of the positive metallic
ons in the solution the more positive will be the charge on the
netal and, conversely, the lower the concentration of the metallic
ons in the solution the more negative will be the charge on the
aetal.

151

152 THE DETERMINATION OF HYDROGEN IONS

Not only metals but various gases are found to act in a similar
way when means are devised to bring them into a situation as
easily handled as are metal electrodes. Hydrogen is one of these
gases and the means of handling it as an electromotively active
gas is to take it up in one of those metals such as platinum, pal-
ladium or iridium which in a finely divided condition hold large
quantities of hydrogen. Platinum black deposited upon plati-
num and laden with hydrogen forms a hydrogen electrode. It
can be brought into equilibrium with hydrogen ions as silver is
brought into equilibrium with silver ions; and the more positive
it becomes the higher must be the concentration of the positively
charged hydrogen ions in the surrounding solution.

It remains however to formulate with mathematical precision
the way in which the potential of the hydrogen electrode changes
with the concentration of the hydrogen ions; and for this purpose
the energy relations must be considered.

Suppose a metal electrode dips into a solution of ions of the
same metal. Let the concentration of these ions be such that
their partial pressure, which would be manifest in an arrangement
for producing osmotic pressure, is P in the volume V.

Let the electrode be of such a size that one gram mol of ions,
carrying nF faraday of electricty, can pass from electrode to
solution to there raise the partial pressure by dP. The increase of
the difference of potential between electrode and solution will be
dE. The electrical work expended will then be nFdE and the
work taken up by the material system will be VdP. If the
process is reversible, and the system is allowed to return to the
original state,

nFdE - VdP = 0

VdP
or dE = -^=-. (26)

We shall now assume that we are dealing with an "ideal solu-
tion" by which we mean a solution in which the pressure-volume
relation of the ions conforms to the gas law for a "perfect gas,"

T>rp

then PV=RT or V = -p .

THEORY OF THE HYDROGEN ELECTRODE 153

Substituting this equivalent of V in equation (26) we have

dE = 5T dP
nFP

On integration this becomes

E = — InP + K (27)

where In is the symbol for natural logarithm to the base e and K
is an integration constant.

The integration constant is the point of reference for the gen-

TJT
eral relation E = — In P. It is the potential difference between

electrode and solution when some arbitrary unit of pressure
is chosen and P = 1. Then in accordance with the unit chosen
E = K.

LeBlanc (1907) and others have substituted for K an equiv-

T»T

alent constant of the form — In p, called p the electrolytic

solution tension of Nernst and so obtained the relation

E = In —

nF p

But it is of doubtful value to postulate the physical signifi-
cance of K in this manner. For present purposes we can afford
to leave K as it stands, a pure integration constant.

Let us consider now the arrangement known as a concentration
cell. Let the two vessels of figure 13 contain the same metal ion
in concentrations C and C corresponding to "osmotic pressures"
P and P'. Let there dip into each solution an electrode of the
metal. Let the two solutions be connected by a siphon, and the
slectrodes by a device for measuring the E. M. F.

Using the equation (27) developed above we know that at elec-

T?T
;rode 1 there will be a difference of potential E = — In P + K and

nF
PT
it electrode 2 a difference of potential E' = — In P' + K. The

154 THE DETERMINATION OF HYDROGEN IONS

total E. M. F. will be the algebraic sum of these potential dif-
ferences. If P' be less than P, the electrode in contact with the
ions at partial pressure P' will be negative to the electrode in
contact with the ions at partial pressure P. Hence

E.M.F. = E-E'= — lnP + K-T— lnP' + K~|= —In--
nF LnF J nF P'

Since the ratio of the pressures may be considered equal to the
ratio of the ion concentrations,

E. M. F. = — In - (28)

nF C

This is the fundamental equation for the E. M. F. of a concen-
tration chain.

R is the gas constant, T the absolute temperature, (273.09+
t centigrade), n the valency of the ion and F the faraday or the
quantity of electricity associated with 1 gram molecule equivalent.

To put this equation into working form there have to be found
the electrical equivalents for R and F. Since measurements of
potential are to be made in terms of the international volt this and
the related units will first be denned as they are given in Bureau
of Standards Circular No. 60 (1916), "Electrical Units and
Standards."

International ohm. The international ohm, which is generally
referred to as the ohm, but which is to be distinguished as are
other international units from the " absolute" units, is denned as
"the resistance offered to an unvarying electric current by a col-
umn of mercury at the temperature of melting ice, 14.4521 grams
in mass, of a constant cross-sectional area and of a length of
106.300 cm."

International ampere. The international ampere, generally re-
ferred to as the ampere, is defined as "the unvarying electric cur-
rent which, when passed through a solution of nitrate of silver
in water in accordance with specification II (of the 1908 London
Conference), deposits silver at the rate of 0.00111800 of a gram
per second."

International volt. The volt is derived from current and re-

E
sistance in accord with Ohm's law, C = — . The international

THEORY OF THE HYDROGEN ELECTRODE 155

volt is therefore denned as "the electrical pressure (electromotive
force) which, when steadily applied to a conductor the resistance
of which is one international ohm, will produce a current of one
international ampere."

F, the faraday, is derived for the international system as fol-
lows. The international ampere deposits silver at the rate of
0.00111800 of a gram per second. Since the atomic weight of
silver is 107.88, a gram equivalent would be deposited in one sec-
ond by 96494 amperes. The coulomb (international) is the quan-
tity of electricity transferred by a current of one international
ampere in one second. Hence 96494 coulombs are carried by a
gram equivalent of silver and this is the value of the faraday in the
international system.1

Returning now to equation (28) we know that R, the gas con-
stant, is derived from the gas equation

P V P V

PV = -£ili T, where -±°12- is R.

273.09 273.09

V0, the volume of 1 gram molecule of an ideal gas at one at-
mosphere pressure and 0°C. is 22412 ± 2 cc. (Berthelot, 1904).
P0 = one atmosphere or 76 cm. of mercury at 0°C. and 45° lati-
tude. Since the acceleration of gravity at 45° latitude was taken
to be 980.665 cm. per second when the "atmosphere" was defined,
and, since 1 cc. mercury under the action of such a gravitational
pull weighs 13.59545 grams, P0 = 980.665 X 76 X 13.59545 or
1013276 dynes per square centimeter.

„ „ . 1013276X22412 ooiCWifto

Hence R is = 83157719.8 ergs.

273.09

107 ergs = one joule absolute. One joule, absolute = 0.99966
international joule. Hence R = 8.3129446 international joules,
or volt coulombs.

From the derivations outlined above our equation reduces to
the numerical form

^ 8.3129446 T . C
E = In —

96494 n C1
1 The absolute value is approximately 96,500 (Vinal and Bates, 1914).

156 THE DETERMINATION OF HYDROGEN IONS

Transposing to Briggsian logarithms (to the base 10) by di-
viding by 0.43429 we have

E = 0.00019837 -log — (29)

n C1

In the case of the hydrogen electrode, where the valence of the
ionic hydrogen concerned is one, n is generally not written.

A table of the values of 0.00019837 T for various tempera-
tures is given in the Appendix.

The significance of the equation for the concentration chain is
that, if T is known, and if the concentration of the ions in the
other solution is known, then the concentration of the ions in one
solution can be determined from the E. M. F. of the chain. Fun-
damentally there is no other way of applying electromotive force
determinations to the estimation of ion concentrations, unless
there can be brought to bear mass action relations. This makes
it necessary to start somewhere in the system with a solution
whose hydrogen ion concentration has been determined by an
independent method.

Let us assume for the moment that the conductivity method
will give us correct information upon the hydrogen ion concen-
tration of some simple solution such as that of HC1.

It will be remembered that hydrogen ion concentrations are
expressed in terms of normality, a solution normal with respect
to hydrogen ions being one which contains in one liter of solu-
tion 1 gram2 of hydrogen ions.

If, then, the normality of the hydrogen ion concentration in
any unknown solution is to be determined it would seem that
the most convenient solution with which to compare the unknown
would be a solution of normal hydrogen ion concentration. Be-
tween a hydrogen electrode in this standard and a hydrogen elec-
trode in the unknown solution of hydrogen ion normality Cx
there would be a difference of potential, E, given by the equation

E = 0.000, 19837 T log -^ (30)

2 It makes little difference whether we regard the atomic weight of
hydrogen as 1.0 or as 1.008 for the purpose at hand.

THEORY OF THE HYDROGEN ELECTRODE 157

A measurement of E and T would give Cx. Now E in the
above equation is the difference between the potential difference
at the one hydrogen electrode and the potential difference at
the other hydrogen electrode. Nothing need be known about
the value of either single potential difference and very little is
known. If the electrode in the normal solution is made the
standard it is obviously convenient for present purposes to call
the potential difference between this electrode and the solution
zero. Thus arises the definition: The 'potential difference between
a hydrogen electrode under one atmosphere pressure of hydrogen and a
hypothetical solution normal with respect to the hydrogen ion shall
be considered to be zero at all temperatures}

Having established by definition the value of the potential
difference at the normal hydrogen electrode it becomes convenient
to speak of the potential difference at any other hydrogen elec-
trode as the hydrogen electrode potential, thus abbreviating the
term "potential difference." It is, of course, implied that such
a "potential" is referred to the potential difference at the normal
hydrogen electrode. To indicate this the symbol Eh is used.

Unfortunately it has* been necessary to introduce into the
definition of the normal hydrogen electrode the phrase u hy-
pothetical solution normal with respect to the hydrogen ion."
This is because that very desirable standard solution would have
to be prepared by means of "strong" acids and the estimation
of the hydrogen ion concentration would fall under those uncer-
tainties which have already been mentioned in a previous chapter.
The difficulty is not entirely obviated by making the experimental
standard a more dilute solution of a strong acid as has been done;
but we shall leave to Chapter XIX further discussion of this
Droblem, and, for the moment, we shall assume that there can be
constructed from measurements such as those of the conductivity
nethod a solution having a definite, known hydrogen ion con-
centration. We could proceed with this, using it as one of two
iolutions in a hydrogen gas cell, and applying to this cell the

3 In various places, notably in the report of the Potential Commission
>f the Bunsen-Gesellschaft (Abegg, Auerbach and Luther, 1910) it is not
pecifically stated that this difference of potential shall be zero at all tem-
peratures, but it seems to have been so understood and is specifically so
; tated by Lewis (1913).

158 THE DETERMINATION OF HYDROGEN IONS

formula relating the E. M. F. to the ratio of the known to the
unknown hydrogen ion concentration. But it is more convenient
to use as a working-standard a calomel half cell (see Chapter
XIII). When this is joined to a hydrogen electrode to form a
calomel-hydrogen cell we need to know the difference of poten-
tial between the calomel half cell and some known hydrogen elec-
trode. Then we can correct the observed E. M. F. by this differ-
ence and consider the corrected E. M. F. to be as if it were that
between two hydrogen electrodes.

Remembering that the mercury of the calomel half cell is posi-
tive to the platinum of the normal hydrogen electrode and that
the platinum of a hydrogen electrode becomes more negative
the more dilute the hydrogen ion concentration, we have the scheme
shown below

8 a

O O ml

p, a ai Total
3 * "' E.M.F.

o JS

J .2

< *

-Mercury of calomel electrode

Eh of calomel electrode
— Pt of normal hydrogen electrode
Ehx of hydrogen electrode X

-Pt of fractional normal hydrogen
electrode X

If E. M. F. is measured and Eh is known, the value of Ehx
is at once obtained. This is the difference of potential between
two hydrogen electrodes and equation (29) applied. In its work-
ing form this equation is:

E.M.F. (observed) - Eh (of calomel half cell) _ . 1 = H ,^s
0.000,198,37T ~ [H+]

The above equation is still incomplete because we have not taken
into consideration the liquid junction potential differences which
exist wherever two unlike solutions are brought into contact. Nor
have we yet considered the effect upon the potential difference at a
hydrogen electrode of a change in the pressure of hydrogen from
the one atmosphere partial pressure specified for the normal hy-
drogen electrode. These two will be considered from the point
of view of corrections to be made. Liquid junction potential
differences, because of their distinct importance, will be treated
in a separate chapter.

THEORY OF THE HYDROGEN ELECTRODE 159

BAROMETRIC CORRECTION

The potential difference between a metal and solution will
vary somewhat with the condition of the metal. A hammered,
twisted or scratched electrode may show a different potential
against a given concentration of its ions than will an electro-
lytically deposited metal. In the case of the hydrogen electrode
it seems to make little difference whether the hydrogen be held
in platinum, palladium or iridium but it does make a consider-
able difference if the surrounding pressure of hydrogen varies. If
we have two hydrogen electrodes immersed in the same solution
at the same temperature but under different pressures of gaseous
hydrogen, we may assume that the concentration of the hydrogen
in one electrode is different from that in the other electrode, and
that the potential difference may be expressed as

E = Ex-E2= — ln[-5li (32)

nF [H]2

in which equation R, T, n, and F have their customary signifi-
cances and [H]i and [H]2 are concentrations of atomic hydrogen in
the electrodes (platinum black). Since n, the valence of hydro-
gen, is 1, it may be omitted.

We may now assume that there is an equilibrium between the
molecular hydrogen about the electrode and the atomic or ionic
hydrogen in, or issuing from, the electrode. This equilibrium
may be expressed in accordance with the mass law as follows :

rxr] y rTTl

— = Kt where [H] = concentration of atomic hydrogen

[H2]

and [H2] = concentration of molecular hydrogen

Whence,

[H] = VkS] (33)

Substituting (33) in (32), we have

E- RT ln VKOH^ _ RT^tH^
F VKt[H2]2 " 2F [H2]2

It should be noted that the factor 2 in this equation does not
:ome from giving hydrogen an effective valence of 2, as has often
)een stated, but from the introduction of equation (33). We

160 THE DETERMINATION OF HYDROGEN IONS

might however derive the equation more directly by the energy
relations and then the factor 2 would enter by reason of the vol-
ume change involved.

If the ratio of pressures is equal to the ratio of gas concentrations

E = — ln^?
2F PH2

If P'H, be one atmosphere and PH2 be expressed in atmospheres

tp RT, 1

E = In — ,OA,

2F PH1 (34)

This is the equation for the difference of potential between a
hydrogen electrode under one atmosphere pressure of hydrogen
(e.g., the normal hydrogen electrode) and a hydrogen electrode
under pressure PH2.

Experimental justification of this equation is found in the
experiments of Czepinski, Lewis and Rupert, Lewis and Randall,
Lewis and Sargent, Ellis, Loomis and Acree and others.

Hainsworth and Maclnnes have studied the effect of pressures
up to 400 atmospheres and taking account of the volume changes
of Hg, calomel, etc. which are negligible for smaller differences
in pressure, they find a linear relation except for a slight deviation
at the higher pressures.

Several writers have felt constrained to emphasize the fact that
in determining the hydrogen pressure from barometer readings
they have subtracted the vapor pressure of the solution. The
emphasis is still advisable, for a considerable number of precise
hydrogen electrode data are published with corrections for baro-
metric pressure on the basis that the normal hydrogen electrode
pressure is one atmosphere including the vapor pressure of the
solution. Corrections should be made to one atmosphere pres-
sure of hydrogen, or else the standard used should be distinctly
specified.

Clark and Lubs (1916) have suggested that a more consistent
standard than that now recognized for the normal hydrogen elec-
trode would be obtained by defining a standard concentration of
hydrogen father than a standard pressure. They used the com-
monly accepted "standard condition" of a gas which is the con-

THEORY OF THE HYDROGEN ELECTRODE 161

centration at 0°C. and 760 mm. pressure. This would bring both
the hydrogen and the hydrogen ions to a concentration basis,
whereas now the one is expressed in terms of concentration and
the other in terms of pressure.
In applying the correction,

T? RT, 1

Ebar. m

2F PH,

it will be remembered that a decrease of the hydrogen pressure
may be considered as a decrease of the electrolytic solution
tension of the hydrogen. Hence under decreased hydrogen pres-
sure the electrode is left more positive.
In the cell

Hg | Hg2Cl2KCl | H+ | Pt | H2

if the hydrogen is under diminished pressure the E. M. F. of the
cell is too low. Hence the correction must be applied to make the
E. M. F. larger than observed. Equation (31) becomes:

E. M. F. + E(bar.) — E(caiome]) __ jt (ok)

.0.00019837 T

To aid in the calculation of pressure corrections it is convenient
to plot a curve giving the millivolts to be added to the observed
E. M. F. for various corrected partial pressures. Tables of correc-
tions from which a chart may be plotted are given in the Appen-
dix. In these tables the barometer pressures given are the cor-
'ected pressures. If hydrogen escapes from about the hydrogen
ilectrode through a trap or other device which exerts back pres-
sure, this pressure must be taken into consideration. Otherwise
t is assumed that the pressure of the hydrogen is that of the
urometer less the vapor pressure of the solution. To obtain the
orrected barometer reading the instrumental calibration of the
instrument is first applied, then the temperature correction (a
■ able of which is given in the Appendix) necessary to bring the
1 eight of the mercury column at temperature t to its height at
1 amperature 0°C. Then there remains the correction for locality
( see tables in Landolt-Bornstein) in order that the pressure may
1 e reduced to the common basis of the "atmosphere," namely, the
I ressure of 760 mm. mercury where the acceleration of gravity is

162 THE DETERMINATION OF HYDROGEN IONS

980.665 cm. per second. The last correction is of significance
only for very accurate measurements and exceptional localities.

For all ordinary cases it may be assumed that the vapor pres-
sure is that of pure water at the temperature indicated.

If the unit pressure is one atmosphere, the partial pressure
must be reduced to atmospheres.

As inspection of the table in the Appendix will indicate, the
barometric correction may be neglected in rough measurements.

REFERENCES
General

Abegg-Auerbach-Luther (1911), Bose (1900), Carhart (1911), Fresenius
(1912), Foa (1906), Hardman-Lapworth (1911-12), Jahn (1901),
Kistiakowsky (1908), Lewis, G. N. (1908, 1913), Lewis-Randall
(1914), Lewis, W. K. (1908), Loven (1896), Michaelis (1910, 1911,
1914), Myers-Acree (1913), Nernst (1889, 1916), Nernst-Wilsmore
(1900), Noyes, Ostwald (1891), Rothmund (1894), Smale (1894),
Stieglitz (1917), Wilsmore (1900).

Gas Constant, R
Berthelot (1904), Nernst (1904), Van Laar (1893, 1921).

Value of the faraday

Vinal-Bates (1914).

Barometer correction

Bose (1900), Czepinski (1902), Ellis (1916), Foa (1906), Hainsworth-Mac-
Innes (1922), Lewis, W. C. (1920), Lewis-Randall (1914), Lewis-
Rupert (1911), Lewis-Brighton-Sebastian (1917), Loomis (1915),
Loomis-Acree (1916), Loomis-Myers-Acree (1917), Ostwald (1893),
Smale (1894), Wilsmore (1901), Wulf (1904).

Condition of hydrogen in electrodes and catalytic activation

Berry (1911), Eggert (1915), Freeman (1913), Harding-Smith (1918),
Hemptinne (1898), Hoitsema (1895-6), Holt (1914), Holt-Eggar-Firth
(1913), LeBlanq (1893), Luther-Brislee (1903), Maxted (1919-1921),
Mond-Ramsay-Shields (1898), Winkelmann (1901).

Null point of potential

Abegg-Auerbach-Luther (1909-1911), Brunner (1909), Freundlich-Makelt
(1909), Goodwin-Sosman (1905), Lorenz (1909), Lorenz-Mohn (1907),
Nernst (1897), Ostwald (1900), Palmaer (1898, 1907), Wilsmore-
Ostwald (1901).

CHAPTER XI
Potential Differences at Liquid Junctions

When two unlike solutions of electrolytes are brought into con-
tact there develops at the junction a potential difference. Since
no important chain can be constructed without involving such a
liquid junction potential, it is of great importance to know the
cause so that the magnitude of the potential may be calculated
or ways devised for its reduction.

The principal cause of the potential difference was attributed
by Nernst to unequal rates of diffusion of ions across the plane
of junction.

It has been found in the study of electrolytic conduction that
under uniform potential gradient different ions move through a
solution with different velocities. The following table taken from
Lewis' A System of Physical Chemistry shows the velocities of a
number of ions in aqueous solution under a potential gradient
of one volt per centimeter. Since in each case the potential gra-
dient is the same and the ionic charge the same it is evident that
the order in which the velocities stand in the table is the order
in which the velocities of free movement will stand.

ION

ABSOLUTE VELOCITY

IN CENTIMETERS PER

SECOND. 18°C.

ION

ABSOLUTE VELOCITY

IN CENTIMETERS PER

SECOND. 18°C.

32.50 10"*
6.70 10"*
4.51 10-*
3.47 10"*
5.70 10"*

17.80 10~*

6.78 10"*

N03

6.40 10-*

CHsCOO

3.20 lO-4

Let it now be assumed that a solution of hydrochloric acid is
placed in contact with pure water of negligible ion content at an
imaginary plane surface. Independently of one another the
ihlorine and the hydrogen ions will tend to migrate across the inter-
'ace and into the water. As shown in the above table the velocity
)f the hydrogen #ion under the influence of a potential gradient

163

164 THE DETERMINATION OF HYDROGEN IONS

is much greater than the velocity of the chlorine ion under the
same gradient, and the relative velocities of free movement must
therefore be in the same proportion. Consequently there will
be established on the water side of the plane an excess positive
charge. This charge will increase until the electrostatic attrac-
tion dragging the slower moving chlorine ions brings them to the
velocity of the hydrogen ions. When this state is reached, as it
is almost instantaneously, there is established a steady potential
difference at the liquid junction. If the water is replaced by a
solution of an electrolyte, we have not only the chlorine and the
hydrogen ions migrating across the boundary into this new solu-
tion, but the ions of this solution migrating into the hydrochloric
acid solution.

In the comparatively simple case where two solutions of differ-
ent concentration of the same binary electrolyte are placed in
contact the following elementary treatment may be used. Let
the concentration of the ions on one side of the interface be C
and on the other side be a lesser concentration C

When migration has established the steady potential E let it

be over an interface of such extent that E is due to the separation

of one faraday. If that fraction of the separated charge which

is carried by the anion is na the work involved in the transport of na

C .

equivalents from C to C is na RT In ^>. Likewise if that fraction of

the charge carried by the cations is nc the work involved in the

transport of nc equivalents from C to C is nc RT In p7,. The

work involved in the separation of the ions as they migrate from
the high to the low concentration is

naRTln— - ncRTln— = EF

c c

Whence

E = (n. - nc) — In — or (n0 - na) —-In — (36)

F C r C

according to which ion moves the faster.

Now the ions being univalent, na, the fraction of the charge car-
ried by the anion, is equal to the fraction N of one equivalent of
anions transported from the cathode to the anode section. Like-

POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS

165

wise n0 is 1-N. The ratio of N to 1-N is equal to the ratio of
the absolute velocities of the ions.

N velocity of anion (Va)

1 — N velocity of cation (Vc)

Whence

and

N =

Va + V,

1-N =

Va + V,
Substituting N for na and 1

, transport number of anion,

, transport number of cation.
N for nc in equation (36)

E=(Va_-LVe) RTlnC
(Va + V0) F C

(37)

Lewis and Sargent (1909) have treated the special case of two
equally concentrated solutions of two binary salts having one ion
in common. Substituting equivalent conductivities as propor-
tional to mobilities they obtain

E^ln^i
F X2

(38)

where Xi and X2 are the equivalent conductivities of two solu-
tions. Applying this equation they obtain the following corre-
spondence between calculated and observed values of E, the
liquid junction potential.

SOLUTIONS IN CONTACT

E (observed)

E (calcu-
lated)

E (OBS.)-
E (CALC.)

).2nKC1-0 2nKC2H30,

).1nKC1-0.1n KC2H302

).2nKC1-0.2n KOH

-0.0080
-0.0074
+0.0170
+0.0165
+0.0004
+0.0192 ±0.0003
-0.0286

-0.0082
-0.0077
+0.016S
+0.0165
+0.0004
+0.0187
-0 0286

0.0002
0.0003
0.0002

).1nKC1-0.1nKOH

0.0000

).2n KC1-0.2n KBr

0.0000

).2n NuC1-0.2n NaOH

I. In KCI-O.In HC1

0.0000

In the more general case limited chiefly by the condition that

166 THE DETERMINATION OF HYDROGEN IONS

all the ions shall have the same valency Planck (1890) deduced
the equation:

E - 5^ ln ^ (39)

where E is the contact difference of potential in volts and £ is
defined by the equation:

ln?-2-ln£
SU2 - Ui m C! i gc2 - ci

V*-^ In^ + ln/02"^1

Ci is the sum of the concentrations of cations and anions in the
more dilute solution and c2 the sum in the more concentrated solu-
tion, w is the valency, R the gas constant, F the faraday, and

Ui = uV + u"c" + . . . .
V, = vV + v"c" + . . . .

and U2 and V2 are similar sums for the second solution. The u'
and v' symbols represent the ion mobilities and the c' symbols
the corresponding ion concentrations.

Besides the limitation noted above this equation is strictly ap-
plicable only to very dilute solutions where dissociation is complete
and it was deduced for the condition of a sharp boundary such
as is not realized in experimental work.

P. Henderson (1907, 1908) therefore considered the connecting
boundary as a series of mixtures of the two solutions in all propor-
tions and deduced a somewhat simpler equation which Cumming
(1912) has modified by introducing the mobilities at the different
concentrations used.

It is of course obvious that the equations given above and many
others of like nature are inapplicable when the solutions placed
in contact are of unknown composition or are very complex.
Br0nsted (1922) has proposed a novel method of approach which
may prove to have some value, but as yet it is untried, and we
are forced to get such comfort as we can find in a deduction from
the above treatment which will be considered presently. But
even in the simple cases where one or another of the equations

POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS 167

apply the experimenter must face the difficulty of maintain-
ing experimentally the conditions for which they were set up.
For instance Chanoz (1906) constructed the symmetrical
arrangement :

Electrode II MR I M'R' I MR II Electrode,
A B

and then, by maintaining a more or less sharp boundary at A by
renewal of the contact, and allowing diffusion to occur at B, he
obtained very definite E. M. F.'s instead of the zero E. M. F.
which the symmetrical arrangement demanded. This time effect
has been noted by Weyl (1905) and has since been frequently
reported, for instance, by Bjerruni (1911), Lewis and Rupert
(1911), Cumming and Gilchrist (1913), Walpole (1914) andFales
and Vosburgh (1918).

Since the change of potential has been ascribed to the diffusion
and mixing which alter the distribution of the contending, mi-
grating ions, it has seemed to many that the effect could be made
more uniform and conditions more reproducible if the solutions
were brought into contact at a membrane. This would tend to
prevent mixing. Sand or other material would also delay the
mixing and the diffusion. Cumming and Gilchrist (1913) used
a symmetrical chain such as that of Chanoz (see above) , and found
that when a membrane was introduced at A while ordinary con-
tact was allowed at B the symmetry of the chain was destroyed.
Prideaux (1914) also found a difference when the contact was
made in the one case with, and in the other case without, a parch-
ment membrane. On considering this case and others in which
the constituents of the membrane may take part in the establish-
ment of the potential, he came to the conclusion that there were
phenomena concerned which made the application of the ordinary
squations of dubious value. See also Beutner (1913).

Lewis, Brighton and Sebastian (1917) using Bjerrum's (1911)
suggestion of a layer of sand in which to establish the liquid con-
act found that "at no time were reproducible results obtained
lor results which remained constant to 0.0001 volt for more than
i minute or two. The potential of the liquid junction first es-
ablished was surprisingly high (0.030 volt) and fell rapidly with-

168 THE DETERMINATION OF HYDROGEN IONS

out reaching any definite limiting value. " The liquids placed in
contact in this experiment were 0.1m HC1 and 0.1m KC1. These
authors abandpned the sand method.

On the other hand Myers and Acree (1913) report satisfaction
with Bjerrum's " Sandfiillung. "

Other devices such as the use of a wick have been resorted to,
but on the whole direct liquid contact is considered the best.

Recently Lamb and Larson (1920) have described the "flowing
junction" which they find to be much more reproducible than
the junctions usually made. They conclude "that a 'flowing'
junction, obtained simply by having an upward current of the
heavier electrolyte meet a downward current of the lighter elec-
trolyte1 in a vertical tube at its point of union with a horizontal
outflow tube, or by allowing the lighter electrolyte to flow con-
stantly into a large volume of the heavier electrolyte, even with
N solutions, gives potentials constant and reproducible to 0.01 of
a millivolt. " The device used by Lamb and Larson is illustrated
in figure 15.

Maclnnes and Yeh (1921) have improved the system of Lamb
and Larson and have confirmed the principle that reproducible
liquid junction potentials may be thus obtained, but they find
most interesting effects with different rates of flow. Of particular
importance is the observation that the reproducible potentials
are not the highest that can be obtained.

It is encouraging to see experimental work of this type being
done for those who are interested in the general applications of
electrode measurements cannot escape the feeling that the ex-
perimental side of the problem has been too much neglected.

A most important contribution to experimental methods of
handling liquid junction potential differences arose from the the-
ory of Nernst that the potential is due to the unequal migration
of ions. The table of velocities given on page 163 will show that
if KC1 is concerned no large potential can arise from the partici-
pation of its ions, because they move with about the same velocity.
If such a salt be present in high concentration upon both or even
one side of the interface, the electrostatic fields of its ions will
dominate the situation, and, migrating at equal velocities, will tend
to maintain zero junction potential difference. Bjerrum (1911)
studied the potential differences developed when concentrated so-

POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS

169

lutions were thus employed and estimated the theoretical values
with the aid of Planck's formula and with that of Henderson,
which purports to take into account the effect of the destruction
of a sharp boundary. He came to the conclusion that the use
of a 3.5m KC1 solution would not completely eliminate the po-
tential against hydrochloric acid solutions but he suggested a
more or less empirical extrapolation which would, he thought,

Fig. 15. Lamb and Larson's Device for the Flowing Junction

j ive the proper correction. The correction is the difference in the
] 1. M. F/s of a chain found when first 3.5m KC1 is used and then
> men 1.75m KC1 is used to connect two electrodes.

More recently Fales and Vosburgh (1918) have made an ex-
t msive comparison of various chains, and with the aid of Planck's
f )rmula to give the order of magnitude of various contact poten-
t als, thay have attempted to assign values which will lead to a
g 3neral consistency. They concur with others in finding Planck's
f irmula invalid in the assignment of accurate values to liquid
j motions, such as:

170 THE DETERMINATION OF HYDROGEN IONS

"xm KC1 - 1.0m HC1 and xu KC1 - 0.1m HC1 where x ranges
from 0.1 to 4.1 and the temperature is 25°C."

They conclude that "there is no contact potential difference at
25° between a saturated solution of potassium chloride (4.1m) and
hydrochloric acid solutions ranging in concentrations from 0.1
molar to 1.0 molar," confirming the suggestion of Loomis and
Acree (1911).

Because of the great detail concerned in the reasoning of Fales
and Vosburgh it is impossible to briefly summarize their work, but
before their conclusion can be considered valid it must be noted
that they themselves point out that "in an electromotive force
combination having a contact potential difference as one of its
component electromotive forces, the diffusion across the liquid
junction of the one liquid into the other brings about a decrease in
the magnitude of the contact potential difference, and this de-
crease may amount to as much as one-tenth of the initial magni-
tude of the contact potential difference. " This experimental un-
certainty undoubtedly renders questionable the comparability,
if not the precision of measurements by different experimenters.
If so there may lurk in the data used by Fales and Vosburgh in
their argument of adjustment to consistency an indefinite degree
of incomparability.

Indeed the whole subject of contact potential is still in an un-
satisfactory state. The experimental uncertainties which have
been revealed have sometimes been overlooked in the calculation
of important electrode values. Some of these values will be dis-
cussed in Chapter XIX.

In writing the components of a chain it is customary to desig-
nate the situation of a potential difference by a single line and
the position of a potential difference which is to be left out of
consideration by a double line. Thus

Pt H2 1 N/10 HC1 1 N/10 KC1 Hg2Cl2 1 Hg

indicates that there are potential differences at the positions
shown by the lines; while if the above chain is written as

Pt H2 1 N/10 HC1 1| N/10 KC1 Hg2Cl2 |Hg

the double line indicates that the liquid junction potential differ-
ence is to be left out of consideration in formulating the E.M.F.

POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS 171

It now remains to determine if possible the order of magnitude
of the contact differences of potential entering into chains used
in the study of physiological solutions and the buffer solutions of
the colorimetric method.

Since the concentrations of the hydrogen and the hydroxyl ions,
which are the most mobile of all ions, are very low in most of these
solutions, the contact potential difference may be expected to be
much less than that found in hydrochloric acid solutions and sim-
ilar solutions of high hydrogen or hydroxyl ion concentrations.
It is the customary practice to employ saturated KC1 in making
the junction or to make the junction first with 3.5m, then with
1.75m KC1 and extrapolate according to Bjerrum. The extra-
polation so indicated generally amounts to only a few tenths of a
millivolt, and in certain cases such as "standard acetate" to only
0.1 millivolt. Although such an extrapolation may be too low or
too high its magnitude indicates that the error is not large.
Furthermore there is found experimentally a drift in contact
potential difference with time which is very much less than that
found, for instance, at the junction sat. KC1— 0.1m HC1. There can
be no doubt that this is indicative of a low potential difference.

As pointed out by Clark and Lubs (1916), it is the difficulty in
dealing with the contact potential of hydrochloric acid solutions
that renders them unsuitable for routine standardization of
hydrogen electrodes.

Practical conclusions reached by experimentation are:

1. For precise E. M. F. measurements combinations having
small liquid junction differences of potential should be used as
far as is practicable.

2. It should be recognized that the E. M. F. of a cell which
derives part of its E. M. F. from a liquid junction potential dif-
ference varies with the time elapsing after the formation of the
liquid junction. Consequently this time should become a part
of the data to be recorded.

3. It is preferable that measurements of E. M. F. be made
directly after the formation of or the renewal of the liquid junction.

4. Since the liquid junction potential difference may vary with
the manner of its formation the effort should be made to effect this
junction in a reproducible way.

5. Reproducible potential differences are given by the flowing
junction in the cases so far tried.

172 THE DETERMINATION OF HYDROGEN IONS

6. Narrow or capillary tubes at the point of liquid junction
should be avoided.

7. An apparatus which permits the renewal of a junction and
its complete removal when cells are left set up together for some
time is preferable to any device such as membranes to protect the
diffusion of solutions into electrode spaces.

8. Membranes at the liquid junction are to be avoided.

9. Wherever permissible saturated KC1 solution should form
one side of a liquid junction.

10. When a concentrated KC1 solution is used to make liquid
junction it should be stated whether the Bjerrum extrapolation
with the use of 3.5m and 1.75m KC1 has been employed or whether
saturated KC1 was used without the Bjerrum extrapolation.

REFERENCES

Abegg-Bose (1899), Beutner (1912), Bjerrum (1905, 1911), Chanoz (1906),
Clarke, W. F.-Myers-Acree (1916), Cremer (1906), Cumming (1912),
Cumming-Abegg (1907), Cumming-Gilchrist (1913), Donnan (1911),
Fales-Vosburgh (1918), Gouy (1916), Ferguson (1916), Henderson, P.
(1907-1908), Lamb-Larson (1920), Lewis-Sargent (1909), Lewis-
Rupert (1911), Loomis-Acree (1911), Loven (1896), Maclnnes (1915),
Maclnnes-Yeh (1921), Melander (1915), Myers-Acree (1913), Neg-
baur (1891), Nernst (1888), Planck (1890), Pleijl (1916), Prideaux
(1914), Reisenfeld (1901), Sackur (1901), Schwyzer (1914), Tower
(1896), Weyl (1905).

CHAPTER XII

Hydrogen Electrodes and Electrode Vessels

For the most part the base of a hydrogen electrode is simply a
piece of platinum foil or wire. If wire is used an end is fused
into a glass tube carrying mercury to form a convenient means
of making contact with the lead of the potentiometer circuit.
The wire may then be wound upon a machine screw to give it a
neat form. If foil is used a piece about 1 sq. cm. is first welded
to a short piece of No. 30 B. S. gauge platinum wire by tapping
the two smartly with the flat end of a punch while they are laid
upon a flat hard surface in the white heat of a blast lamp. Next
draw off a glass tube to a thin, blunt point and break away the
capillary until the wire will enter. Slip the wire in until the foil
touches the glass. Then, holding the wire with foil uppermost,
rotate the tube with the junction in the tip of a fine flame. Let
the glass fuse until a perfect seal is made and a little of the glass
fuses to the edge of the foil. The steps are illustrated in figure
16. It is important to avoid a seal with too thin a glass junc-
tion, for such a seal will easily crack. It is likewise important

Fig. 16. Construction of Simple Electrode

to avoid too heavy a junction for proper annealing then becomes
difficult. To anneal hold the electrode directly after its construc-
tion in a smoky flame and gradually remove to cooler and cooler
parts of the flame. If a light but substantial junction is made
with the edge of the foil the electrode will be rugged.

In place of the platinum foil gauze is sometimes successfully
used. The advantage is a larger surface; but gauze will make a
careful technician nervous over the problem of thoroughly clean-
ing the crevices.

173

174 THE DETERMINATION OF HYDROGEN IONS

It is sometimes assumed that complete equilibrium can be at-
tained only when the hydrogen in the interior of the metal sup-
porting the platinum black is in equilibrium with that on the,
surface. To reduce the time factor of this soaking-in process it
is considered advantageous to use as the supporting metal a very
thin film of platinum or iridium deposited upon glass. Doubt-
less the finest of such films could be deposited by holding the glass
tangent to the Crookes' dark space of a vacuum discharge and
spattering the metal on from electrodes under 5000 volts difference
of potential. The method practiced is to burn the metal on from a
volatile solvent. The recipe given by Westhaver(1905) is as fol-
lows: 0.3 gram iridium chloride moistened with concentrated HC1
is dissolved in 1 cc. absolute alcohol saturated with boric acid.
To this is added a mixture of 1 cc. Venetian turpentine and 2 cc.
lavender oil. The glass after being dipped in this solution is
rotated while drying to give an even deposit. It should then be
very carefully dried to prevent blistering during the ignition.
On gradually heating over an alcohol flame there is at last produced
a very thin film of iridium. The process should be repeated
until a good conducting film is obtained.

Gooch and Burdick (1912) have better success with a viscous
mixture of pure chloroplatinic acid and glycerine. This is ap-
plied with an asbestos swab to the glass which has previously
been heated to a temperature which will instantly volatilize the
glycerine. The resulting film is heated until it adheres well
to the glass.

Meillere (1920) gives the following recipe. 0.5 gram dry
platinum chloride is triturated with 10 or 15 grams of essence of
camomile. The mixture is thinned with about an equal volume
of methyl alcohol.

If after some practice it is found that even deposits can be
formed by one or another of the methods, the next difficulty met
is in obtaining good adherence of the film to the glass. This
must be done by heating sufficiently but at the same time there
must be avoided a fusion of such extent that the continuity of
the metallic film will be destroyed. Such a fusion will be more
easily avoided and at the same time volatilization of impurities
in the film will be made easier because of the higher temperature

HYDROGEN ELECTRODES 175

permitted, if the glass support is made of a "hard" glass. How-
ever, in the selection of such a glass one with a temperature
coefficient of expansion approximately equal to the platinum
should be selected, — chiefly as a provision for the next step which
will now be described.

The chief technical difficulty in the preparation of electrodes
with the films described is in establishing the necessary electrical
connection. An exposed platinum wire contact destroys the
object in using the film. Ordinarily the electrode is made by first
coating a bar of glass in the end of which there is sealed a plati-
num wire and then fusing this bar into the end of a glass tube so
that the platinum contact is exposed within the tube where
mercury contact may be made. Connection with the film is made
by the film of metal that runs through the glass seal. It is less
clumsy to seal the wire into the end of a glass tube, break off
the wire flush with the glass, coat the tube with the film and
then close over the exposed wire with a drop of molten glass.

A scheme which is said to partially accomplish the purpose
of a thin film of supporting metal is to cover a platinum support
with a gold-plate, gold being relatively impervious to hydrogen.
It is doubtful whether this reason has much practical weight.
However a gold-plate is of great advantage. If offers a surface
upon which deposits of "black" adhere well. It forms a support
easily dissolved by electrolysis in hydrochloric acid, thus provid-
ing an easy means of removing old deposits. And the character
of the gold deposit gives an additional means of testing the clean-
liness of the electrode prior to blackening.

For the gold plating of electrodes the following recipe may be
used. Dissolve 0.7 gram gold chloride in 50 cc. water and pre-
cipitate the gold with ammonia water, taking care to avoid an
excess. Filter, wash and dissolve immediately in a KCN solution
consisting of 1.25 grams KCN in 100 cc. water. Boil till the solu-
tion is free from the odor of ammonia.

DEPOSITION OF "BLACK"

According to the work of earlier investigators and the con-
sensus of opinion among more recent investigators there seems to
be no difference under equilibrium conditions between coatings of
platinum-, iridium- or palladium-black. No recent detailed data

176 THE DETERMINATION OF HYDROGEN IONS

are available however. Of the three, iridium is recommended by
Lewis, Brighton and Sebastian because of its higher catalytic ac-
tivity, and palladium by Clark and Lubs (1916) for use in the
study of physiological solutions because of the relative ease with
which one deposit may be removed before the deposition of the
next in the frequent renewals which are often necessary. Pal-
ladium black is easily removed by electrolysis in HC1. Deposits
of platinum or iridium may be removed by electrolysis in HC1
solution, if they are deposited upon a gold plate.

One of the essentials for making good deposits is a very high
degree of cleanliness of the electrode. • A good test is the evenness
with which bubbles of hydrogen escape from the surface during
electrolysis. Another essential in the preparation of a good elec-
trode is that the deposit of black metal be not only even but of
proper thickness. The inclination is to make the deposit too
thick, with the production of a sluggish electrode. To obtain
evenness of deposit it is necessary to hold down the dimensions
of the electrode, provide more than one lead, or modify the rate
of deposit. With this much said there remains very little system-
atized information upon the composition of solutions and the
current densities which are best for the deposition of the finely
divided metal required.

For the deposition of platinum black Ellis (1916) uses a solution
of pure chloroplatinic acid containing 1 per cent Pt. He cau-
tions against the use of the lead acetate which has come down to
us in recipes for the deposition of platinum black upon electrodes
for conductivity measurements. For the deposition Ellis uses a
small auxiliary electrode and a current large enough to liberate
gas freely at both electrodes. He continues the deposition with
five-minute reversals of current for two hours and obtains a very
thick coating. The author prefers an adherent, even, thin de-
posit sufficient to just cover the glint of metal beneath. In com-
parison of one against another in the same solution such thin de-
posits are found to agree within 0.02 millivolt. They may be
deposited within a minute from the solutions used by the author.

For the deposition of iridium Lewis, Brighton and Sebastian
(1917) make the gold or gold-plated electrode the cathode in a
5 per cent solution of iridium chloride. "The best results were
obtained with a very small current running for from twelve to

HYDROGEN ELECTRODES 177

twenty-four hours. Too large a current gives a deposit which
appears more like platinum black and which is easily rubbed off. "

The author has used deposits of platinum, iridium and palla-
dium upon platinum, upon gold-plated platinum and upon "rho-
tanium" alloy. Acidified (HC1) 3 per cent solutions of the chlorides
of each metal are used without much attention to the exact
strength. The current from a four- volt storage battery is allowed
to produce a vigorous evolution of gas. The. electrode is plunged,
immediately after the deposition, into a dilute sulfuric acid solu-
tion and electrolyzed. It is required that the bubbles of hydro-
gen then escaping come off evenly, that the electrode be evenly
covered with the deposit in thickness sufficient to cover the glint
of polished metal, and that the deposit shall adhere under a vigor-
ous stream of water. No electrode is ever subjected to blast
lamp treatment as is sometimes recommended. Instead, renewals
are made by removing the old deposit by electrolysis in HO
solution, and, if any defect whatsoever develops to prevent a
good redeposition after such electrolysis, the electrode is retired
from duty.

It must be admitted that the above description is loose.
This is because the rush of experimental application has prevented
a detailed examination of conditions, and experience has taught
details difficult to formulate in exact language. No detailed
descriptions have been found in the literature and those that are
found are quite inadequate to account for the varied deposits some-
times formed. One item which it would be interesting to investi-
gate is the influence of the hydrogen ion concentration of the
solution upon the character of the deposit. Since there is a
simultaneous deposit of metal and hydrogen and, since the char-
acter of the platinum, palladium or iridium black is undoubtedly
due to the vigor of the hydrogen evolution, it is evident that the
pH of the solution constitutes a -part of the conditions.

It may be said however, that ordinarily there is little difficulty
in obtaining an active deposit if the metal concentration is main-
tained as the solution is used, if electrodes are kept thoroughly
clean and if the solutions are kept free from even those impurities
which collect as a film upon exposed solutions. To remove these
films suck them off with a clean tube attached to a filter pump.

The system used by the author for deposition of "black" is

178 THE DETERMINATION OF HYDROGEN IONS

as follows. A row of small vessels, such as weighing bottles
about 2 cm. diameter and 5 cm. deep are fitted with electrodes.
These electrodes are all attached through binding posts mounted
on a wooden rail. These in turn are connected to one pole of
a double-pole, double-throw switch. The opposite pole is con-
nected with a flexible lead tipped with platinum. This lead is
used to connect with the electrodes to be treated. Tl>e middle
connections of the double-throw switch are connected with a
4-volt storage battery. The other connections are cross-wired.
One of the vessels is filled with hydrochloric acid made by a
one-to-one dilution of ordinary 37 per cent acid. This is used
to dissolve previous deposits with the aid of electrolysis (switch
reversed, treated electrode +)• Another vessel is filled with 10
per cent sulfuric acid for preliminary direct and counter-electrol-
ysis in testing the cleanliness of the electrode. Another vessel
is filled with the platinum, palladium or iridium chloride solution.
When using palladium so-called reagent palladium is used as +
electrode and this is removed from the solution when not in use.
After deposition of the black the electrode under treatment is
quickly placed under a vigorous stream of water and then elec-
trolyzed in a another vessel of freshly prepared ten per cent sul-
furic acid until thoroughly charged with hydrogen.

When used with inorganic solutions which undergo no decom-
position electrodes may often be used repeatedly, provided they
are kept clean and not allowed to dry. When there is any sign
or suspicion of an electrode becoming clogged, poisoned, worn,
dry or in any way injured, there should be not the slightest hesi-
tation in reblackening or even rejecting it. It is therefore not
good practice to so tie up a particular electrode with an expensive
stopper or vessel that there will be hesitation in rejecting it.

HYDROGEN ELECTRODE VESSELS

So many types of vessel have been published that it is diffi-
cult to do justice to the advantages of each. The selection must
depend in some instances upon the material to be handled, but in
any case there are a few principles which it is hoped will be made
clear by a discussion of a few of the more widely used vessels.

The general method of operation is to partially or wholly im-

HYDROGEN ELECTRODES

179

merse the electrode in the solution to be measured and then to
bubble hydrogen through the vessel till constant potential is
attained. The vessel described by Lewis, Brighton and Sebastian
(1917) and illustrated in figure 17 is representative of the general
type of vessel used for what may be called the classic mode of
operation. The following is the quoted description of this vessel :

Fig. 17. Hydrogen Electrode Vessel of Lewis, Brighton and

Sebastian

Hydrogen from the generator enters at A, and is washed in the bubbler
B with the same solution that is contained in the electrode vessel. This
efficient bubbling apparatus saturates the gas with water vapor, so that
the current of hydrogen may run for a long period of time without changing
the composition of the solution in the main vessel. The gas rises from the
tip C, saturating and stirring the whole liquid from G to F, and leaves the
apparatus through the small trap E, which also contains a small amount
of the same solution. The platinum wire attached to the electrode D is
sealed by lead glass into the ground glass stopper M. L is a joint made by
fusing together the end of the platinum wire and the connecting wire of
copper. The surface of the solution stands at the height F so that the
iridium electrode is about one-half immersed. The apparatus from F
through G, H, I to J is filled with the solution. With the form of construc-
tion shown it is an easy matter to fill the tube without leaving any bubble?

180 THE DETERMINATION OF HYDROGEN IONS

of air. The reservoir K filled with the same solution serves to rinse out
the tube I, J from time to time. The whole apparatus may be mounted
upon a transite board, or for the sake of greater mobility, may be held in a
clamp, the several parts being rigidly attached to one another to avoid
accidental breakage. The whole is immersed in the thermostat about to
the point L.

The tube J dips into an open tube through which communication is made
to other electrode vessels. This connecting tube may be filled with the
same solution as is contained in the hydrogen electrode vessel or with any
other solution which is desired. All measurements with acids are made
with one of the stopcocks H, I, closed. These stopcocks are not greased
and there is a film of acid in the closed stopcock which suffices to carry the
current during measurement. In Order to make sure that no liquid poten-
tial is accidentally established, the second stopcock may be closed up and
the first opened. No difference of potential in acid solution has ever been
observed during this procedure (but this is not true for solutions of salt
and alkalies). If it is desired that both stopcocks be open, the same
liquid that is in the electrode vessel is placed in the connecting tube at J
and the stopcocks H and I are opened after the current of hydrogen has been
cut off by the stopcock A, and the opening of the trap E has been closed.

If hydrogen enters the cell at the rate of one or two bubbles per minute
several hours are required for the saturation of the solution and for the
removal of air. After this time the potential is absolutely independent of
the rate of flow of hydrogen and the generator may be entirely cut off for
many hours without any change.

For some biochemical studies such a vessel is unsuitable. It
is sometimes absolutely essential that equilibrium potentials be
established rapidly. The necessity is perfectly apparent when one
is dealing with an actively fermenting culture. It is not always
so apparent when dealing with other solutions, but it is suspected
that absolutely complete equilibrium is never attained in some
complex biochemical solutions and that we have to depend upon
speeding up the reaction between hydrogen and hydrogen ions till
a virtual equilibrium point is attained (see Chapter XVII) .

It was shown by Michaelis and Rona (1909) that a fairly con-
stant E. M. F. is quickly attained, even in blood, if the platinized
electrode, previously saturated with hydrogen, is allowed to merely
touch the surface of the solution. This is probably due, as sug-
gested by Hasselbalch (1913) and again by Konikoff (1913), to a
rather sharply localized equilibrium at the point of contact. Re-
ductions and gas interchanges having taken place within the small
volume at the point of contact, diffusion from the remaining body
of the solution is hindered by the density of the surface layer
with which alone the electrode comes in contact.

HYDROGEN ELECTRODES 181

In exploring new fluids it appeared hazardous to the writer to
rely upon such a device, which appears to take advantage of only
a localized and hence a pseudo-equilibrium, and which makes no
allowance for a possible difference between the solution and sur-
face film in the activity of the hydrogen ions. Hasselbalch's
(1911) principle seemed therefore to be more suitable.

Hasselbalch found that a very rapid attainment of a constant
potential can be obtained by shaking the electrode vessel. Un-
der these conditions there should be not only a more rapid inter-
change of gas between the solution, the gaseous hydrogen, and
the electrode, an interchange whose rapidity Dolezalek (1899)
and Bose (1900) consider necessary, but the combined or molec-
ular oxygen, or its equivalent, in the whole solution should
be more rapidly brought into contact with the electrode and there
reduced. Furthermore, by periodically exposing the electrode the
hydrogen is required to penetrate only a thin film of liquid before
it is absorbed by the platinum black. The electrode should there-
fore act more rapidly as a hydrogen carrier. For these reasons a
true equilibrium embracing the whole solution should be rapidly
obtained with the shaking electrode; and indeed a constant
potential is soon reached.

Eggert (1914-1915) in Nernst's laboratory made a study of the
rapidity of reduction by hydrogen electrodes in which he com-
pared the effect of alternate immersion and exposure to the hydro-
gen atmosphere with the effect of continued immersion. In the
reduction of metal salt solutions such as ferric salts he obtained
a much greater velocity of reduction when the electrode was
periodically removed from the liquid carrying a thin film of solu-
tion to be exposed to the hydrogen. The maximum velocity
was proportional to the platinum surface and the time of contact
with the gas. It was independent of the number of times per
ninute the electrode was raised and lowered. As the reaction
leared completion the decrease in velocity of reaction became
exponential.

Making use of the principles brought out in the preceding dis-
cission and also certain suggestions noted in the chapter on liquid
unction potentials Clark (1915) designed a vessel which appears
o have found favor for general use. A working drawing of this
ressel is shown in figure 18. If solutions more viscous than fresh

182

THE DETERMINATION OF HYDROGEN IONS

milk are to be used, the bores of the inlet and outlet tubes
should be made larger. If only very small quantities of the solu-
tions to be tested are available, the dimensions of the vessel
may be reduced. In figure 19 is a diagrammatic sketch of the
complete system now in use by the author for ordinary work.

(ron no. o stopper)

/eo°

Fig. 18. A Hydrogen Electrode Vessel (Clark, 1915)

Notes. In submitting this working drawing to a glass blower it shall be
specified that: (1) Cocks shall be joined to chamber with a neat and wide
flare that shall not trap liquid. (2) Cocks shall be ground to hold high
vacuum. (3) Bores of cock keys shall meet outlets with precision. (4)
The handles of keys shall be marked with colored glass to show positions of
bores. (5) The handles of both keys shall be on the same side (front of
drawing). (6) Vessel shall be carefully annealed. (7) Opening for no. 0
rubber stopper shall be smooth and shall have standard taper of the stand-
ard no. 0 stopper. (8) Dimensions as given shall be followed as closely as
possible. (9) No chipped keys or violation of the above specifications
shall be accepted.

HYDROGEN ELECTRODES

183

•iiiuimiiiiiiua

Ll hill im!|,.||i

Q
O

a
o
M

184 THE DETERMINATION OF HYDROGEN IONS

The electrode vessel is mounted in a clamp pivoted behind the
rubber connection between J and H. This clamp runs in a groove
of the eccentric I, the rotation of which rocks the vessel. In the
manipulation of the vessel, the purpose is, first, to bring every
portion of the solution into intimate contact with the electrode
F and the hydrogen atmosphere, to make use of the principle of
alternate exposure and immersion of electrode and then, when
equilibrium is attained, to draw the solution into contact with
concentrated KC1 solution and form a wide contact at H in a
reproducible manner. The E. M. F. is measured directly after
the formation of this liquid junction.

The vessel is first flooded with an abundance of hydrogen by
filling the vessel as full as possible with water, displacing this
with the hydrogen, and then flushing with successive charges of
hydrogen from the backed-up generator. Water or solution is
run into the vessel from the reservoir D which can be emptied
through the drain B by the proper turning of the cock C. Solu-
tion or hydrogen displaced from the vessel is drained off at B'.
These drains when they leave the electrical shielding (see p.
231) should hang free of any laboratory drain.

With the vessel rocked back to its lowest position the solution
to be tested is run in from D (after a preliminary and thorough
rinsing of the vessel with the solution) until the chamber E is about
half full. Cock G is closed and cock C is turned so as to permit a
constant pressure of hydrogen from A to bear upon the solution.
For very careful work it is well to bubble hydrogen through the
solution. The rocking is then commenced and is continued until
experience shows that equilibrium is attained with the solution of
the type under examination. The eccentric I should give the
vessel an excursion which will alternately completely immerse the
electrode F and expose it all to the hydrogen atmosphere. The
rate of rocking may be adjusted to obtain the maximum mixing
effect without churning.

To establish the liquid junction the rubber tube between J and
H is pinched while G is turned to allow KC1 solution to escape at
B'. Then a turn of G and the release of the pinch draws the solu-
tion down through the cock to form a broad mixed junction at H.
For a new junction the old is flushed away with fresh KC1 from the
reservoir N by properly setting cock L.

HYDROGEN ELECTRODES 185

With the closed form of calomel electrode, M, shown in the figure
no closed stopcocks need be interposed between the terminals of
the chain. With the customary calomel electrode vessel it is
necessary to use a closed cock somewhere and since this must be
left ungreased it is well to have it a special cock1 at J.

If a tube be led out from J and branched, several hydrogen
electrode vessels may be joined into the system. At all events it
is well to work with two vessels in parallel so that one may be
flushing with hydrogen while the other is shaking.

The electrode F is supported in a sulfur-free rubber stopper.
A glass stopper may be ground into place but is seldom of any
advantage and may prove to be a mistake. In the first place it
is advisable to be free with electrodes and to instantly reject any
which fail to receive a proper coating of metal. The inclination to
do this is less if it entails the rejection of a carefully ground stop-
per. Unless the stopper is accurately ground into place it is
worthless. Furthermore it is very difficult to so grind a glass
stopper that there will be left no capillary space to trap liquid. A
rubber stopper can be forced into place without leaving such a
space. The rapidity with which measurements are usually taken
makes it improbable that a rubber stopper, if made sulfur free,
can have any appreciable effect. If the rubber must be pro-
tected a coating of paraffine will do.

The calomel electrode M is of the saturated type so that no
particular care need be taken to protect it from the saturated KC1
used in making junctions. This is the working standard for the
accurate standardization of which there is held in reserve the
battery of accurately made, tenth-normal, calomel electrodes P.
This battery may be connected with the system at any time by
making liquid connection at 0 and opening K. After a measure-
ment the liquid junction is eliminated, the space rinsed with the
tenth normal KC1, and liquid contact left broken.

The design of this system is obviously for an air bath. The
necessity of raising cocks out of an oil bath would not permit
such direct connections as are here shown.

1 To make an easily turning cock out of which KC1 will not creep, grease
the narrow part of the socket and the wide part of the key. When the key
is replaced there will be two bands of lubricant on which the key will ride
with an uncontaminated zone between for the film of KC1 solution.

186 THE DETERMINATION OF HYDROGEN IONS

Fig. 20. Types of Hydrogen Electrode Vessels

HYDROGEN ELECTRODES 187

In figure 20 are shown several other designs of electrode vessels.
A is one of the original Hasselbalch vessels which have since been
modified for the use of replaceable electrodes. B (S0rensen), (Ellis)
and C (Walpole), are operated in a manner similar to the vessel
shown in figure 18. Walpole 's vessel was made of silica and the
electrode was of platinum film as described on page 174. D (Mc-
Clendon and Magoon) was designed for determinations with small
quantities of blood. E (Michaelis) , employs a stationary hydrogen
atmosphere and a wick connection for the liquid junction. G (Long)
is a simple device which the designer thought applied the essential
principles of Clark's vessel. Barendrecht 's vessel, H, is designed for
immersion in an open beaker for estimations during titrations.
It is similar to a design of Walpole 's (1914), but is provided with
a plunger the working of which permits the rinsing of the bulb and
the precise adjustment of the level of the liquid. Another immer-
sion electrode is Hildebrand's, F, the successful operation of which
depends upon a vigorous stream of hydrogen, which, on escaping
from the bell surges the solution about the electrode. A modifi-
cation which provides better protection of the electrode from
oxygen is Bunker's design, I.

At this point it may be of interest to note that Wilke (1913) at-
tempted to make a hydrogen electrode by using a thin tube of pal-
ladium on the interior of which hydrogen was maintained under
pressure. One of the difficulties with such an electrode is the
estimation of the hydrogen pressure at the solution-electrode in-
terface. Wilke 's idea has never been developed to a practical
point so far as we know, but it is worthy of study as an im-
mersion electrode for industrial use.

For titrations where exact control of liquid junction potential
differences is of relatively less importance than control of wastage
of the material titrated, the system illustrated in figure 21 is
useful. Titrations are carried on in the Erlenmeyer flask
which is held in place by the plate P. The arm carrying the
spring may be attached to the support at A in a variety of ways.
It may be bolted, riveted or screwed; but should be made with
a "running fit" so that while held firmly, it may be turned to
permit removal of the Erlenmeyer. The plate F should be rigidly
attached to the support at B. In this plate there is turned a
hole tapered to receive snugly the rubber stopper which holds

188

THE DETERMINATION OF HYDROGEN IONS

the various attachments. If this hole is left rough from the lathe

tne various attachments. 11 tms noie is leit rough trom the lathe
tool the stopper will be held very firmly after the various glass

Fig 21. A Hydrogen Electrode Vessel Suitable for Titrations

tubes have been forced into place. ' The support has been illus-
trated* in the drawing as if it were at the left. As a matter of fact
it is behind the vessel, and carries at E a bar which supports the

HYDROGEN ELECTRODES 189

calomel cell K. The supporting system is illustrated roughly for
there are various constructions which may be used. In the
author's apparatus A is a screw connection and the junctions at B
and E are riveted and soldered.

It is of course essential that the solution be shaken after each
step of the titration. If the support is clamped to a somewhat
flexible rod the whole system may be shaken. Otherwise the
glass vessel should be protected from the metal of the supporting
plate by an inset of asbestos wood and then, if the spring is not
too stiff, the vessel alone may be swirled. During a titration
cock M is kept closed and N is left open. If the system is suffi-
ciently rigid, if care is used in the operation of the cocks and if
serious temperature changes are avoided very little of the solu-
tion will be drawn into the capillary S and very little of the KC1
will run or diffuse into the solution.

A wire form of electrode will withstand shaking and possible
scraping better than a foil electrode.

Hydrogen is delivered beneath the surface of the liquid. At
the first flushing an abundance of hydrogen is used; later but little
is necessary. The hydrogen escapes through a tube not shown and
should be run through a trap having a shallow layer of water.

The burette tip shown in the figure is lengthened by a piece
of capillary tubing.

If the hydrogen be replaced by purified nitrogen and if the
platinized electrode be replaced by a gold-plated electrode this
vessel does very well for oxidation-reduction titrations. In this
case the nitrogen is delivered above the solution and not below the
surface.

In some cases a preliminary reduction of a solution may be
accomplished by making the solution, in the presence of hydrogen,
travel down a long spiral of platinized wire. The spiral is made
by winding no. 24 copper wire closely upon a rod, mounting it
with a spread of the turns just sufficient to hold together descend-
ing drops, plating with gold and then platinizing. Liquid de-
livered slowly at the top of the spiral will be broken into drops
which in the descent of the spiral are thoroughly stirred. The
reduced solution is brought into contact with an electrode in a
constricted part of the enclosing tube and is then delivere'd to a
continuous-flow liquid junction such as that described by Lamb

190 THE DETERMINATION OF HYDROGEN IONS

and Larson or Maclnnes (see page 168). The hydrogen by suit-
able devices may be given the carbon-dioxid partial pressure of
the tested solution. Such a scheme is useful only in dealing with
continuous treatment processes where abundance of material
is available.

Keller (1922) has described a hydrogen electrode with a re-
placeable disk of platinum gauze. This is held by a cap to a hard
rubber support which contains a portable calomel electrode. The
system is rugged and may be used as an immersion chain for
determining the pH values of liquids in commercial processes.

In conclusion it may be said that with ordinary care almost any
simple combination of electrode and electrode vessel will give
fairly good results. On the other hand it is often necessary not
only to provide against continuous loss of CO2 from biological
solutions but also to arrange for rapid attainment of equilibrium.
Since electrode measurements are often the last resort, since one
can easily be misled by pseudo-equilibria and since attention to a
few simple details of construction and operation frequently in-
creases very greatly the speed of experimentation, the "simplicity"
of certain designs is sometimes more apparent than real.

However it would be invidious to select any particular design
for criticism, the more so because none yet published is perfectly
adapted to all purposes. Those described are therefore to be
considered as illustrations from which the reader may select items
or suggestions to incorporate in his own design.

SUPPLEMENTARY REFERENCES

Bailey (1920), Baker-Van Slyke (1918), Barendrecht (1915), Bose (1900),
Bunker (1920), Dolezalek (1899), Eggert (1914-1915), Ellis (1916),
Gooch-Burdick (1912), Clark (1915), Cullen (1922), Hasselbalch
(1910-1913), Hastings (1921), Hildebrand (1913), Hudig-Sturm (1919),
Konikoff (1913), Lewis-Brighton-Sebastian (1917), Linhart (1919),
Long (,1916), Loomis-Acree (1911), Maloney (1921), McClendon (1915,
1916, 1918), McClendon-Magoon (1916), Michaelis (1910, 1911, 1914),
Michaelis-Rona (1909), Myers-Acree (1913), Peters (1914), Rudnick
(1921), Sand-Law (1911), S0rensen (1909), Sturm (1918), Treadwell-
Weiss (1920), Walpole (1913, 1914), Westhaver (1905), Wilke (1913).

CHAPTER XIII
Calomel Electrodes

Unless otherwise specified the calomel electrode is an electrode
in which mercury and calomel are overlaid with a definite concen-
tration of 'potassium chloride. For particular purposes HC1 calo-
mel electrodes or those containing some other chloride are used.

The general type of construction is shown by A, fig. 23. A layer
of very pure mercury is covered with a lajer of very pure calomel
and over all is a solution of a definite concentration of KC1 satu-
rated with calomel.

The difference of potential between mercury and solution is
determined primarily by the concentration of the mercurous ions
supplied from the calomel. But, since there is equilibrium be-
tween the calomel, the mercurous ions and the chlorine ions, the
concentration of the mercurous ions is determined by the chlorine
ion content furnished chiefly by the KC1. One of three concentra-
tions of KC1 is usually employed — either 0.1 molecular, 1.0 molecu-
lar or saturated KC1. These are ordinarily referred to as the
"tenth normal-," "normal-" or "saturated calomel electrodes."

The mercury used in the preparation of these electrodes or
"half-cells" should be the purest obtainable. In Chapter XV
methods of purification are described. Sufficient mercury should
be used to cover the platinum contact deeply enough to prevent
solution reaching this contact on accidental shaking.

More portable half-cells are made by amalgamating a plati-
num wire or foil. This is done by electrolyzing a solution of
nercurous nitrate, the wire being the negative pole. Provision
s then made for keeping a paste of calomel about this wire.

Some success has been attained with the use of the better
grades of calomel supplied on the market but the risk is so great
hat it is best to prepare this material in the laboratory. A
shemical and an electrolytic method will be described.

The chemical 'preparation of calomel. Carefully redistill the best
•btainable grade of nitric acid. Dilute this slightly and with it
lissolve some of the mercury prepared as described in Chapter

191

192 THE DETERMINATION OF HYDROGEN IONS

XV, always maintaining a large excess of mercury. Throw the
solution into a large amount of distilled water making sure that
the resulting solution is distinctly acid. Now, having distilled
pure hydrochloric acid from a 20 per cent solution and taken the
middle portion of the distillate, dilute and add it slowly to the
mercurous nitrate solution with constant stirring. When the
precipitate has collected, decant and treat with repeated quanti-
ties of pure distilled water (preferably conductivity water). The
calomel is sometimes washed, with suction upon a Buchner funnel
but if due regard be taken for the inefficiency of washing by de-
cantation it is preferable to wash repeatedly by decantation since
there is thereby obtained a more even-grained calomel. Through-
out the process there should be present some free mercury.

Electrolytic preparation of calomel. Doubtless the better prepa-
ration of calomel is formed by electrolysis according to the method
of Lipscomb and Hulett (1916), This is carried out in the same
way that the mercurous sulfate for Weston cells is formed. For
the preparation of mercurous sulfate Wolff and Waters (1907)
employ the apparatus shown in figure 22. An improvised appa-
ratus may be made of a glass tube with paddles, platinum wire
electrode and mercury contact and with two spools for bearing
and pulley. In place of the sulfuric acid there is used normal
hydrochloric acid. A direct current (from a four-volt storage
battery) must be used. The alternating current sometimes used
in the preparation of mercurous sulfate does not seem to work in
the preparation of calomel according to some* preliminary experi-
ments which Mr. McKelvy and Mr. Shoemaker of the Bureau of
Standards kindly made for the writer. During the electrolysis the
calomel formed at the mercury surface should be scraped off by
the paddles c and c (fig. 22). The calomel formed by this process
is heavily laden with finely divided mercury.

Calomel formed by either the chemical or the electrolytic proc-
ess should be shaken with repeated changes of the KC1 solution
to be used in the half -cell before the calomel is placed in such a
cell.

The variations in the potentials of calomel electrodes have been
the subject of numerous investigations. Richards (1897) ascribed
it partly to the formation of mercuric chloride. Compare Rich-
ards and Archibald (1902). Sauer (1904) on the other hand con-

CALOMEL ELECTRODES

193

eluded that this had little to do with the inconstancy. Arguing
upon the well known fact that the solubility of slightly soluble
material is influenced by the size of the grains in the solid phase,
Sauer thought to try the effect of varying the grain size of the calo-
mel as well as the effect of the presence of finely divided mercury.

Fig. 22. Wolff and Waters' Apparatus for the Electrolytic
Preparation of Mercurous Sulfate or of Calomel

With cells made up with various combinations he found the fol-
lowing comparisons :

Hg- calomel

against

calomel

Hg+ =

- 0.00287 volt

(fine) (coarse)

(fine)

(coarse)

Hg~ calomel

against

calomel

Hg+ =

- 0.00037 volt

(fine) (coarse)

(coarse)

Hg- calomel

against

calomel

Hg+ -

- 0.0025 volt

(coarse) (coarse)

(fine)

(coarse)

194

THE DETERMINATION OF HYDROGEN IONS

Fig. 23. Types of Calomel Electrode Vessels

CALOMEL ELECTRODES 195

Lewis and Sargent (1909) state that they do not confirm Sauer
in regard to the effect of the finely divided mercury but that they
do confirm him in regard to the state of the calomel. These au-
thors and others recommend that grinding the calomel with mer-
cury to form a paste be avoided as this tends to make an uneven
grain. It is better to shake the mercury and the calomel together
but this is unnecessary if electrolytic calomel is used.

Here and there in the literature we find various other sugges-
tions such as the elimination of oxygen from the cell ; but there
seems to be no very substantial agreement in regard to this and
several other matters as there is no substantial agreement in the
preference of one concentration of KC1 over another. By the use
of carefully prepared material and the selection of the better agree-
ing members of a series, calomel electrodes may be reproduced to
agree within 0.1 millivolt or better; but it has not yet been estab-
lished whether or not this represents the order of agreement among
electrodes made in different laboratories. Furthermore there
still remains the question of the effect of minor disturbances.
There is no question that "true" values are not to be expected
until all parts of the system are in equilibrium and that a prelimin-
ary shaking such as Ellis uses will hasten the attainment of equilib-
rium. On the other hand a disturbance which will alter the
surface structure of the mercury exposed may produce a slight
temporary shift in the potential difference. The subject remains
'or systematic investigation.

The most extensive investigation of unsaturated calomel elec-

rodes was made by Acree and his students (Myers and Acree,

joomis and Acree), but how far the reproducibility which they

ittained by short circuiting the differences of potential is repre-

: entative of the general reproducibility of such electrodes is not

; ret established.

In figure 23 are shown several calomel electrode vessels each
' rith a feature that may be adapted to a particular requirement.
Valpole's (1914) vessel, A, is providedwith a contact that leads
< ut of the thermostat liquid and with a three-way cock for flushing
i way contaminated KC1. A more elaborate provision for the
] rotection of the KC1 of the electrode is shown in the vessel of
1 -ewis, Brighton and Sebastian (1917), B. A form useful as a sat-
i rated calomel electrode in titrations is shown at C. Fresh KC1

196 THE DETERMINATION OF HYDROGEN IONS

passes through the U-tube to take the temperature of the bath
and to become saturated with calomel shown at the bottom of
this U-tube. D is Ellis' (1916) vessel, which in the particular
form shown was designed to be sealed directly to the remainder of
the apparatus used. A valuable feature is the manner of making
electrical contact. Instead of the customary sealed-in platinum
wire Ellis uses a mercury column. On closing the cocks the ves-
sel may be shaken thoroughly to establish equihbrium. This
feature has not been generally practiced. Vessel E is a simple
form useful for the occasional comparison electrode. It may be
made by sealing the cock of an ordinary absorption tube to a
test tube and adding the side arm. F is the vessel of Fales and
Vosburgh (1918) with electric contact made as in the familiar
Ostwald vessel (G).

In adding new KC1 solution to a vessel it must be borne in mind
that the solution should be saturated with calomel before equihb-
rium can be expected. It is well therefore to have in reserve a
quantity of carefully prepared solution saturated with calomel.

Lewis, Brighton and Sebastian (1917) state that certain grades
of commercial KC1 are pure enough to be used in the preparation
of KC1 solutions for the calomel electrode while other samples
"contain an unknown impurity which has a surprisingly large
effect upon the E. M. F. and which can only be eliminated by
several recrystallizations. " It is therefore obvious that the only
safe procedure, in lieu Of careful testing by actual construction of
electrodes from different material, is to put the best available KC1
through several recrystallizations.

Acree has called attention to the possible concentration of the
KC1 solution by the evaporation of water and its condensation on
the walls of vessels unequally heated in thermostats.

The values assigned to the potential differences at the several
calomel electrodes at different temperatures vary. A judicious
selection will wait upon the consideration of several important
matters. Some of the more important of these will be presented
in Chapter XIX. At this point however we may recount with-
out comment some of the more frequently used values which the
reader may choose to use.

Clark and Lubs (1916) give the following compilation of Bjer-
rum's values and those of S0rensen and Koefoed published by
S0rensen (1912):

CALOMEL ELECTRODES

197

TABLE 42

Bjerrum

S0rensen and Koefoed
Bjerrum

S0rensen and Koefoed.

TEMPERATURE

°c.
0

18
20

30
40
50
60
75

POTENTIAL DIFFERENCE BE-
TWEEN NORMAL HYDROGEN
ELECTRODE AND N/10 CALOMEL
ELECTRODE WHEN HYDROGEN
PRESSURE IS

Oneatmosphere

less vapor

pressure

volts

0.3366

0.3377
0.3375

0.3367

0.3364
0.3349
0.3326
0.3290
03243

One

atmosphere

volts

0.3367

0.3380
0.3378

0.3371

0.3370
0.3359
0.3344
0.3321
0.3315

In the report of the "Potential Commission" of the Bunsen-
Gesellschaft (Abegg, Auerbach and Luther, 1911) the normal hy-
drogen electrode standard of difference of potential was adopted.
This of course is only incidental except as temperature coefficients
enter. The differences of potential between the normal hydrogen
electrode and the tenth-normal and normal KC1 calomel electrodes
were given as 0.337 and 0.284-0.283 respectively. .Auerbach
(1912) in a review of this report called attention to the smaller
temperature coefficient of the potential difference at the tenth-
normal calomel electrode when referred to the normal hydrogen
electrode (as having zero potential difference at all temperatures)
and suggested that the tenth-normal electrode be taken as the
working standard with the value 0.3370 between 20°C. and 30°C.

Loomis and Acree (1911) present a choice of values for the
tenth-normal calomel electrode at 25°C. referred to the normal
hydrogen electrode. The choice depends upon the ionization as-
cribed to the hydrochloric acid solutions used in their hydrogen
electrodes and upon the values of the contact differences of poten-
tial which were involved. Loomis (1915) i? inclined to accept the
/alue 0.3360.

198 THE DETERMINATION OF HYDROGEN IONS

In 1914 Lewis and Randall applied " corrected degrees of dis-
sociation" to the hydrochloric acid solutions used in arriving at
the difference of potential at 25° between calomel electrodes and
the theoretical normal hydrogen electrode. Denning the normal
calomel electrode as the combination Hg Hg2Cl2, KC1 (1M), KC1
(0.1 M) they reach the value 0.2776. The difference of potential
between this electrode and the tenth normal they give as 0.0530.
Whence the value for the tenth normal electrode is 0.3306. These
values were revised by Lewis, Brighton and Sebastian (1917)
to 0.2828 for the difference of potential between the normal
calomel and the normal hydrogen electrode, and 0.0529 for the
difference between the normal and the tenth normal.

Beattie (1920) using more recent data calculates for the poten-
tial difference at the normal calomel electrode 0.2826 and com-
pares this value with 0.2824 which is Lewis, Brighton and Se-
bastian's result (see above) when corrected by Beattie for the
liquid junction potential difference between 0.1 N and 1 N KC1.

It will have been noted that in measurements with the hydro-
gen electrode there is no concern for the absolute difference of
potential between mercury and solution. This is because the calo-
mel half-cell is merely a convenient go-between for measurements
in which one hydrogen electrode is compared with another. For
this reason it is convenient to retain the "normal hydrogen elec-
trode" standard of reference and it so happens that this is in
harmony with a general though not universal custom adopted
for all electrode measurements.

Other systems are: first, that in which the difference of poten-
tial between the mercury and a normal concentration of KC1 in
a calomel electrode is taken arbitrarily as zero, and second that
in which this difference of potential is given what is considered
to be its actual value.

Largely upon the basis of Palmaer's (1903) work the value 0.560
volt has been used as the "absolute" difference of potential
between mercury and N/1 KC1 saturated with calomel in the
presence of solid calomel at 18°C. (The mercury being positive
to the solution.) There is some skepticism1 regarding the re-

1 Whether this is just or unjust is a question concerning which we
are in doubt. No critical review in the light of modern researches is known
to the author.

CALOMEL ELECTRODES 199

liability of this value, but for the particular purpose with which
we are now concerned it makes little difference what the value
is if proper relative relations are maintained. But the difficulty
in maintaining proper relative relations when there is no agree-
ment on a standard basis of reference is made evident when we
consider that the temperature coefficient for the absolute differ-
ence of potential between mercury and solution is very different
from the temperature coefficient for the difference of potential
between calomel electrode and hydrogen electrode when the
normal hydrogen electrode is defined as having zero potential
difference at all temperatures. Thus, as shown by Fales and
Mudge (1920), the absolute temperature coefficient of the satur-
ated calomel half-cell is low and has a positive value. But the
temperature coefficient of the values for the saturated calomel
half-cell as used in hydrogen electrode work is negative and
high. Fales and Mudge seem not to have made any independent
measurements which furnish more reliable values for the differ-
ence of potential between a saturated calomel half-cell and the
"normal hydrogen electrode." These authors have however
extended the work of Michaelis and have found evidence that
the saturated calomel half-cell is reliable within the temperature
interval 5°-60°C.

As a working standard the saturated calomel half-cell is un-
doubtedly the best as pointed out by Michaelis and Davidsohn
(1912). It does not require careful protection from the saturated
KC1 solution usually employed as a liquid junction and it has a
high conductivity permitting full use of the sensitivity of a low-
resistance galvanometer. It differs in no way from other calomel
half-cells except that the solution is saturated with KC1 in the
presence of solid KC1 at all temperatures used.

There is not very good agreement between the values assigned
bo the saturated calomel half-cell by different laboratories and it
lad therefore best be regarded for the time being as a good work-
ng-standard to be checked from time to time against carefully
nade normal or tenth normal calomel electrodes or against a
lydrogen electrode in a standard solution. For ordinary meas-
urements however the values given in table a of the Appendix
„re adequate.

200

THE DETERMINATION OF HYDROGEN IONS

Michaelis (1914) gives the following table of values for the po-
tential differences referred to the normal hydrogen electrode for
the tenth normal and the saturated calomel electrodes.

TABLE 43

TEMPERATURE

TENTH NORMAL

SATURATED

0.2525

0.2517

0.2509

0.3377

0.2503

0.2495

0.3375

0.2488

0.2482

0 2475

0 2468

0 2463

0.2458

0.3364

0.2355

0.3355

0.2350

0.3349

0.3326

0.3290

SUPPLEMENTARY REFERENCES

Abegg (1902), Abegg-Auerbach-Luther (1909), Auerbach (1912), Bjerrum
(1911), Bugarszky (1897), Clarke-Myers-Acree (1916), Coggeshall
(1895), Coudres (1892), Ellis (1916), Fales-Vosburgh (1918), Lewis-
Brighton-Sebastian (1917), Lewis-Sargent (1909), Lipscomb-Hulett
(1916), Loomis (1915), Loomis-Aeree (1911), Loomis-Meacham (1916),
Michaelis (1914), .Michaelis-David off (1912), Myers-Acree (1913),
Newberry (1915), Palmaer (1907), Richards (1897), Richards-Archi-
bald (1902), Sauer (1904), Steinwehr (1905). See also Chapter XIX
for potential values.

CHAPTER XIV
The Potentiometer and Accessory Equipment

The method usually employed in the measurement of potential
differences is the Poggendorf compensation method, the poten-
tiometer method. In principle it consists in balancing the poten-
tial difference under measurement against an opposing, known
potential difference. When the unknown is so balanced no cur-
rent can flow from it through a current-indicating instrument such
as a galvanometer.

The principle may be illustrated by the arrangement shown in
figure 24 which is suitable for very rough measurements.

According to modern theory the conduction of electricity in
metals is the flow of electrons, the electron being the unit electrical
charge. By an unfortunate chance the two kinds of electricity,
which were recognized when a glass rod was rubbed with silk,
were given signs (+ for the glass and — for the silk) which now
leave us in the predicament of habitually speaking of the flow of
positive electricity when the evidence is for the flow of negative
charges, the electrons. But so far as the illustration of principles
is concerned it makes little difference and we shall depart from
custom and shall deal with the negative charges in order to make
free use of a helpful analogy. We may imagine the electrons,
already free in the metal of our electrical conductors, to be com-
parable with the molecules of a gas which if left to themselves
will distribute themselves uniformly throughout their container
(the connected metallic parts of our circuits). We may now im-
agine the battery S (fig. 24) as a pump maintaining a flow of
gas (electrons) through pipes (wires) to R to A to B and back to
S. The pipe (wire) AB offers a uniform resistance to the flow
so that there is a uniform fall of pressure (potential) from A to
B while the pump (battery) S maintains a uniform flow of gas
(electrons). If we lead in at C and at D the ends of the pipes
'wires) from another pump (battery) X, taking care that the
ligh pressure pipe (wire) from X leads in on the high pressure
dde of AB, we can move C, D or both C and D until they span

201

202

THE DETERMINATION OF HYDROGEN IONS

a length of AB such that the difference of pressure (difference of
potential) between C and D on AB is equal and opposite to the
difference of pressure (difference of potential) exerted between
C and D by X. Then no current can flow from X through the
current-indicating instrument G and we thereby know that
balance is attained.

If we know the fall of electrical potential per unit length along
AB the difference of potential exerted by X will be known from
the length of wire between C and D. We now come to the man-
ner in which this fall of potential per unit length is determined.

I I I I I I I I i i I i i i

Fig. 24. Elementary Potentiometer

Choosing for units of electrical difference of potential, electrical
resistance and electrical current, the volt, the ohm, and the am-
pere respectively, we find that they are related by Ohm's law:

,. N Difference in potential (in volts)

Current (in amperes) = — — : ; :

Resistance (in ohms)

(41)

With this relation we could establish the fall of potential along
AB by measuring the resistance of AB and the current flowing.
But this is unnecessary, for we have in the Weston cell a standard

THE POTENTIOMETER 203

of electromotive force (E. M. F.) which may be directly applied
in the following manner. The unknown X (figure 24) is switched
out of circuit and in its place is put a Weston cell of known E. M. F.
Adjustment of C and D is made until the "null point" is attained,
when the potential difference between the new positions of C and
D is equal to the E. M. F. of the Weston cell. From such a setting
the potential fall per unit length of AB is calculated. It must be
especially noted however that for such a procedure to be valid the
current in the potentiometer circuit must be kept constant between
the operations of standardization and measurement for the fundamen-
tal relationship upon which reliance is placed is that of Ohm's law

C = — . It will be noted that the establishment of the difference
R

of potential between any two points on AB by the action of S
and the resistance of AB is strictly dependent upon the relation
given by Ohm's law; but, since we draw no current from X when
balance is attained, the resistance of its circuit is of no funda-
mental importance. It only affects the current which can flow
through the indicating instrument G when the potential differ-
ences are out of balance. It is therefore concerned only in the
sensitivity of G.

The simple potentiometer system described above is susceptible
to refinement both in precision and in convenience of operation.

With the inevitable variations in the potentiometer current
which occur as the battery runs down it would be necessary to
recalculate from moment to moment the difference of potential
per unit length of the wire AB if the procedure so far described
were used. This trouble is at once eliminated if the contacts of
the Weston cell can be thrown in at fixed points and the current
be then adjusted by means of the rheostat R so that there is always
the same uniform current producing, through the resistance be-
tween the Weston cell contacts, the potential difference of this
standard cell. Having thus arranged for the adjustment of a
uniform current at all times and having the resistance of AB
already fixed it is now permissible to calibrate the wire AB in
terms of volts.

In the Leeds and Northrup potentiometer (fig. 25), the resist-
ance AB of our elementary instrument (fig. 24) is divided into two
sections one of which A-D (fig. 25) is made up of a series of

204

THE DETERMINATION OF HYDROGEN IONS

resistance coils between which M makes contact and the other
portion of which is a resistance wire along which M' can slide.
When the potentiometer current has been given the proper value,
in the manner which will be described, the fall of potential across
any one of the coils is 0.1 volt so that as M is shifted from the
zero point D the potential difference between M and D is increased
0.1 volt at each step. Likewise, when the current is in adjust-
ment, the shifting of M' away from D increases by infinitesimal
known fractions of a volt the difference of potential between M
and M'.

+OscO-

+ OEMfO-

GA. O

Fig. 25. Wiking op the Leeds and Northrup Potentiometer (Type K)

Now to adjust the potentiometer current so that the several re-
sistances in the potentiometer circuit will produce the differences
of potential in terms of which the instrument is calibrated, use is
made of the Weston cell in the following manner. By means of
a switch, U, the unknown is thrown out and the Weston cell is
thrown into circuit. One pole of the Weston cell circuit is fixed
permanently. The other can be moved along a resistance at T
constructed so that the dial indicates the value of the particular
Weston cell in use. When so moved to agree with the particular
cell in use, this contact at T is left in its position. Now the current
flowing from the battery W is adjusted by means of the rheostat R

THE POTENTIOMETER

205

until the difference of potential between T and 0.5 balances the
potential difference of the Weston cell as indicated by the cessation
of current in the galvanometer GA. The resistance T to "0.5" is
such that the E. M. F. of the battery acting across this resistance
will produce the desired potentiometer current. This current
now acting across the several resistances furnishes the indicated
potentials, i.e., a potential difference of 0.1 volt across each coil.
Another arrangement which employs the ordinary sets of re-
sistances in common use is illustrated in figure 27.

Fig. 26. The Leeds and Northrtjp Potentiometer

A and B are duplicate sets of resistances placed in series with
the battery S. If the current be kept uniform throughout this
system the potential difference across the terminals of B can be
varied in accordance with Ohm's law by plugging in or out resist-
ance in B. But to keep the current constant while the resistance in
B is changed a like resistance is added to the circuit at A when it
is removed from B, and removed from A when it is added to B.

As mentioned before, the potential difference could be deter-
mined from the resistance in B and a measurement of the current
but this is avoided by the direct application of a Weston cell of
known potential. Assuming constant current a Weston cell
replaces X and adjustment to the null point is made by alter-
ing the resistance in B with compensation in A. The unknown
is then thrown into circuit and adjustment of resistance again

206

THE DETERMINATION OF HYDROGEN IONS

made to the null point. If Ew is the known E. M. F. of the Wes-
ton cell, Ex the potential of the measured cell, Rw the resistance
in circuit when the Weston cell is in balance and Rc the resistance
in circuit when the measured cell is in balance we have

Whence

C (constant) = — = — -
Rc Rv

Ex =

EWRC
Rw

(42)

Fig. 27. Elementary Resistance Box Potentiometer System

The system is improved by providing means of regulating the
potentiometer current till constant difference of potential is at-
tained between terminals at which a Weston cell may be thrown
into circuit. Then the resistances may be calibrated in volts.

It will be noted that in this arrangement every switch or plug
contact is in the potentiometer circuit. A bad contact, such as may
be produced by failure to seat a plug firmly during the plugging
in and out of resistance, or by corrosion of a plug or dial contact,
will therefore seriously affect the accuracy of this potentiometer
system. It requires constant care.

THE POTENTIOMETEB 207

Lewis, Brighton and Sebastian (1917) used two decade resist-
ance boxes of 9999 ohms each. With an external resistance the
current was adjusted to exactly 0.0001 ampere. Thus each ohm
indicated by the resistance boxes when balance was attained cor-
responded to 0.0001 volt. Their standard cell which gave at 25°
1.0181 volts was spanned across B (fig. 27) and 182 ohms of the
external resistance.

Another mode of using the simple system illustrated in figure
24 is a device frequently used by physicists, and introduced into
hydrogen electrode work by Sand (1911) and again by Hilde-
brand (1913). Instead of calibrating unit lengths along AD
by means of the Weston cell, or otherwise applying the Weston
cell directly in the system, the contacts C and D carry the terminals
of a voltmeter. When balance is attained this voltmeter shows
directly the difference of potential between C and D, and there-
fore the E. M. F. of X.1

A diagram of such an arrangement is shown in figure 28. There
is an apparent advantage in the fact that the Weston cell may be
dispensed with and resistance values need not be known. There
are however serious limitations to the precision of a voltmeter and
in two cases which the author knows accuracy within the limited
precision of the instruments was attained only after recalibration.

A voltmeter is generally calibrated for potential differences
imposed at the terminals of leads supplied with the instrument.

Turning again to figure 24 we recall that when any given fall
of potential occurs between A and B, a definite current flows in
the circuit SRAB. If the resistance of AB is known a measure
of the current flowing permits one to calculate the fall of potential
between A and B. Thus a current-measuring instrument (am-
meter) placed in series with the fixed resistance AB may be cali-
brated to indicate differences of potential between A and B.

1 It is sometimes assumed that because the circuit of the system under
measurement is placed in the position of a shunt on the potentiometer cir-
cuit that its resistance must be high in order that CD (fig. 24) may indicate
correctly the potential difference. The fact that no current flows in this
branch when balance obtains shows clearly that its resistance can have no
effect on the accuracy of the indication. It has also been assumed that if
CD is spanned by a voltmeter, the resistance of the voltmeter should be
taken into consideration. But a voltmeter is calibrated to always indicate
the potential difference between its terminals.

208

THE DETERMINATION OF HYDROGEN IONS

To use this system the terminals of the gas chain C and D (fig.
24) are moved to A and B and there permanently fixed. An
ammeter is placed between R and S and adjustment of R is made
until no current flows in G. The difference of potential between
A and B as indicated by the calibrated and renamed reading of
the ammeter is then equal to the E. M. F. of the gas chain.

Much the same limitations noted in the voltmeter system apply
to the ammeter system.

Fig. 28. Voltmeter Potentiometer System

A modification of the system briefly described above is found
in the "Pyrovolter." The essential modification is a device of wir-
ing whereby the same indicating instrument is used to measure
current (indicated in volts) and to indicate the null point.

In a few instances there has been employed a system of measure-
ment, the principle of which is illustrated in the wiring diagram
of figure 29. The E. M. F. of a gas chain is allowed to charge
a fixed condenser c. By throwing the discharge key to the right
the charge accumulated by the condenser is allowed to discharge
through a ballistic galvanometer b, the deflection in which may be
made a measure of the accumulated charge and hence of the
E. M. F. of the gas chain.

THE POTENTIOMETER

209

The ballistic galvanometer is one designed to indicate by the
angular deflection of its coil the quantity of electricity passing
through the coil as a sudden discharge. The quantity of elec-
tricity stored in the condenser is a function of its dimensions
and material and of the difference of potential imposed at its

hEMFh

■'ig. 29. Wiring Diagram Used in the Ballistic Galvanometer System

erminals. The dimensions and material being fixed the charge
■ecomes proportional to the difference of potential. Now a
( efinite difference of potential may be imposed by means of the
Veston cell w. The resulting charge in the condenser is discharged
■ hrough the ballistic galvanometer giving the coil a definite
( eflection. This serves to calibrate a given set-up if the galva-
) ometer is so designed that the deflection at each section of the

210 THE DETERMINATION OF HYDROGEN IONS

scale is proportional to the quantity of electricity discharged
through the coil and if the wiring be such that no serious changes
of capacity and inductance occur in manipulation.

The advantage of. this condenser method is that the condenser
may be conveniently made of such capacity that insignificant
current is drawn from the cell under measurement. If then the
technique used at the electrodes is refined it should be possible
to measure equilibrium potentials which would be easily dis-
placed by current withdrawal. However, until there are pub-
lished more definite data relating the conditions of electrode
measurements to the theory of the condenser method, this system
is not to be recommended for ordinary use. In a few instances
when the potentiometer had already been ad j used to the potential
of a gas chain the author has observed what appears to be an
excessive E. M. F. unsupported by the equilibrium conditions
under measurement. This disappears after an initial throw of the
galvanometer and would not be apparent if the measurement were
being made by adjusting the potentiometer from an original
position sufficiently out of balance to permit a very sb'ght current
to flow during successive taps of the key. Will such E. M. F/s,
which are evidently temporary and do not represent the equilib-
rium conditions under measurement, be recorded in the ballistic
galvanometer method?

Goode (1922) has used the 3-electrode vacuum valve in an
arrangement for following the electromotive forces of gas chains.

The 3-electrode electron tube is the instrument used as detec-
tor and amplifier in radio-communication and is known by various
names such as "the audion." A glass bulb (fig. 30) exhausted
to a very low gas pressure is supplied with an atmosphere of elec-
trons by their emission from the hot filament F. These electrons
produce what may be called a space charge in the bulb. Surround-
ing the filament is a metallic plate P which can be maintained at
a potential about 22 volts more positive than the filament by
means of the battery B. Under the influence of this fall of po-
tential electrons migrate from filament to plate, producing the
so-called plate-current. But interposed in this electron-drift
is a grid, G, of wire or perforated sheet metal through which the
electrons must pass in their migration from filament to plate.
If this grid is charged positively with relation to the filament it

THE POTENTIOMETER

211

will tend to neutralize the space charge and so assist the filament-
to-plate current. Conversely, if the grid is charged negatively
with relation to the filament, it will assist the space charge
and so tend to oppose the filament-to-plate current.

Thus the potential difference between filament and grid, a
potential difference which may be impressed by a gas chain or
other cell, can govern in large measure the filament-to-plate stream
of electrons and a measure of this current can be made a measure
of the E. M. F. of the cell, C.

•I' H*£

Fig. 30. Wiring of Goode's System Employing the Electron Tube

Goode considers the plate current Ip to be made up of a con-
stant current IQ characteristic of a given bulb and set working
conditions and a current Ip — IG which is a function of the poten-
tial difference induced by C. To balance I0 Goode found that
with the particular bulb he used it was sufficient to place a vari-
able resistance R between the positive terminal of the A battery
and the negative terminal of the B battery and to adjust this
resistance till the galvanometer Ga was at its zero setting. Under
these circumstances the deflection of Ga becomes a function of the

212 THE DETERMINATION OF HYDROGEN IONS

grid potential. Within the range of E. M. F. of the cells under
study Goode found that with his particular apparatus the de-
flection of Ga was a linear function of IP — I0 when Ga was shunted
by a resistance r such that one large scale division corresponded
to one unit of pH.

Goode claims that the unique advantage of his system consists
in the fact that so little current is drawn from the cell C that
continuous readings may be made. This system should, there-
fore, prove useful in studying those drifts of electrode potential
which occur in a variety of cases and which need more thorough
investigation.

For the more refined uses to which Goode's system may be
put it will be necessary either to know the characteristics of the
bulb in use or else to carefully calibrate a given apparatus.

The electron tube, when used as a valve for amplification,
should be useful in making hydrogen electrode differences of
potential control mechanical devices such as alkali or acid feeds
for continuous commercial processes.

NULL POINT INSTRUMENTS

Referring to figure 24 and the accompanying text the reader will
see that in the balancing of potential differences by the Poggen-
dorf compensation method there is required a current indicating
instrument to determine the null point. Such instruments will
be briefly described, and some of their characteristics discussed.

The galvanometer is a current-indicating instrument, which, in
the form most useful for the purpose at hand, consists of a coil of
wire in the magnetic field of a strong permanent magnet. This
coil is connected into the circuit in which the presence or absence
of current is to be detected. A current flowing through the turns
of the suspended coil produces a magnetic field in its interaction
with the field of the permanent magnet and tends to turn the coil
so that it will embrace the maximum number of lines of force.
The construction of galvanometers need not be discussed since it
is a matter for instrument makers, but certain desirable qualities
will be treated in a later section, together with the characteristics
of other instruments.

Provision should be made for the mounting of a galvanometer

THE POTENTIOMETER

213

where it will receive the least vibration. If the building is sub-
jected to troublesome vibrations some sort of rubber support
may be interposed between the galvanometer mounting and the
wall bracket or suspension. Three tennis balls held in place by
depressions in a block of wood on which the galvanometer is
placed may help. In some instances the more elaborate Julius
suspension such as those advertised may be necessary.

Fia. 31. A Galvanometer

The capillary electrometer depends for its action upon the altera-
ion of surface tension between mercury and sulfuric acid with
.Iteration of the potential difference at the interface. A simple
orm suitable for that degree of precision which does not call for
he advantages of a galvanometer is illustrated in figure 32.

Platinum contacts are sealed into two test tubes and the tubes
j re joined as illustrated by means of a capillary K of about 1 mm.
( iameter. In making the seals between capillary and tubes the
( apillary is first blown out at each end and can then be treated as
i tube of ordinary dimensions in making a T joint. After a thor-

214 THE DETERMINATION OF HYDROGEN IONS

ough cleaning the instrument is filled as illustrated with clean, dis-
tilled mercury, sufficient mercury being poured into the left tube
to bring the meniscus in the capillary near a convenient point.
In the other tube is now placed a solution of sulfuric acid made
by adding 5.8 cc. water to 10 cc. sulfuric acid of 1.84 specific
gravity. The air is forced out of the capillary with mercury
until a sharp contact between mercury and acid occurs in the
capillary. The instrument is now mounted before a microscope
using as high power lenses as the radius of the glass capillary will
permit. The definition of the mercury meniscus is brought out
by cementing to the capillary with Canada balsam a cover glass
as illustrated.

An important feature in the use of the capillary electrometer
is its short circuiting between measurements. This is done by the
key shown in figure 32. Tapping down on the key breaks the short-
circuit and brings the terminals of the electrometer into circuit
with the E. M. F. to be balanced. If the E. M. F. is out of bal-
ance the potential difference at the mercury-acid interface causes
the mercury to rise or fall in the capillary. Releasing the key
short-circuits the terminals and allows the mercury to return to
its normal position. Adjustment of the potentiometer is con-
tinued till no movement of the mercury can be detected. To
establish a point of reference from which to judge the movement
of the mercury meniscus the microscope should contain the fa-
miliar micrometer disk at the diaphragm of the eye piece. In
lieu of this an extremely fine drawn thread of glass or a spider web
may be held at the diaphragm of the eye piece by touches of Can-
ada balsam.

The quadrant electrometer is so little used as a null point instru-
ment that only a brief description will be given. In the form
useful for the purpose at hand a very light vane of aluminium is
suspended by an extremely fine thread, preferably of quartz,
which is metalized on the surface in order to conduct charges to
the vane. The vane is surrounded by a flat, cylindrical metal
box cut into quadrants. Two opposite quadrants are connected
to one terminal and the remaining quadrants to another terminal.
If now the vane or needle be charged from one terminal of a
high-voltage battery the other terminal of which is grounded,
and a difference of potential be established between the two sets

THE POTENTIOMETER

215

of quadrants, the needle will be deflected by the electrostatic
forces imposed and induced. When used as a null point instru-
ment in connection with the potentiometer the two sets of quad-
rants may be connected as are the terminals of the capillary
electrometer and spanned by a short-circuiting key.

Fig. 32. Diagram of Capillary Electrometer and Key

Since the current drawn for its operation is only the amount
lecessary to charge a system of very low capacity to the low po-
ential difference when the potentiometer is slightly out of bal-
ance with the measured E. M. F. (and to zero potential difference

216 THE DETERMINATION OF HYDROGEN IONS

at balance) the quadrant electrometer might be of special value
in the study of easily displaced, electrode equilibria. However,
the attainment of the desired sensitivity with some of these in-
struments is a task requiring great skill and patience. Further-
more the rated sensitivity is sometimes attained by adjusting the
so-called electrostatic control to such a value that the zero posi-
tion of the needle is rendered highly unstable. This combined
with the very long period at high sensitivity renders the instru-
ment unsatisfactory for common use. Against these objections
are: first, the point mentioned above, and second the advantage
that the instrument may ordinarily be left in circuit during the
adjustment of the potentiometer as is not the case with the
galvanometer.

Telephone receiver. The modern high resistance telephone re-
ceiver of the type used in radio reception may serve in an emer-
gency [Kiplinger (1921)]. Lack of balance between potentiometer
adjustment and measured E. M. F. is indicated by a click in the
receiver when the potentiometer key is tapped; but there is of
course nothing but the loudness of the click to show how far from
balance the adjustment is, and only the decrement of the sound
to indicate that adjustment in the proper direction is being made.

Selection of null point indicators. In the selection of instru-
ments for the measurement of the electromotive force of gas
chains it is desirable that there should be a balancing of instru-
mental characteristics and the selection of those best adapted to
the order of accuracy required. A null point instrument of low
sensitivity may annul the value of a well-designed, expensive and
accurate potentiometer; and a galvanometer of excessive sensi-
tivity may be very disconcerting to use. The potentiometer sys-
tem and the null point instrument should be adapted one to the
other and to their relation to the system to be measured.

The several corrections which have to be found and applied to
accurate measurements of hydrogen electrode potentials are
matters of a millivolt or two and fractions thereof. Collectively
they may amount to a value of the order of 5 millivolts. Whether
or not such corrections are to be taken into account is a question
the answer to which may be considered to determine whether a
rough measuring system or an accurate one is to be used. For all
"rough" measurements the capillary electrometer is a good null

THE POTENTIOMETER 217

point instrument. It has a very high resistance which hinders
the displacement of electrode equilibria at unbalance of a crude
potentiometer system. It is easily constructed by anyone with
a knowledge of the elements of glass blowing, and without par-
ticular care may be made sensitive to 0.001 volt.

For "accurate" measurements there is little use in making an
elaborate capillary electrometer or in temporizing with poor
galvanometers.

The apportionment of galvanometer characteristics is a compli-
cated affair which must be left in the hands of instrument makers,
but there are certain relations which should be fulfilled by an in-
strument to be used for the purpose at hand, and general knowledge
of these is quite necessary in selecting instruments from the wide
and often confusing variety on the market.

Galvanometer sensitivities are expressed in various ways.
Since one's attention is centered upon detecting potential differences
the temptation is to ask for the galvanometer sensitivity in terms
)f microvolt sensitivity. There are two ways of expressing this
vhich lead to different values. One is the deflection caused by a
nicrovolt acting at the terminals of the galvanometer. The
nore useful value is the deflection caused by a microvolt acting
hrough the external critical damping resistance. But in the last
analysis the instrument is to be used for the detection of very
! mall currents and these currents when allowed to flow through the
j ;alvanometer by the unbalancing of the circuit at a slight poten-
lial difference are determined by the total resistance of the gal-
vanometer circuit. The instrument might be such that a micro-
volt at the terminals would cause a wide deflection, while, if
1 Dreed to act through a large external resistance, this microvolt
^ 'ould leave the galvanometer "dead. " For this reason it is best
t d know the sensitivity in terms of the resistance through which a
i nit voltage will cause a given deflection. This is the megohm
sensitivity and is defined as "the number of megohms (million
c hms) of resistance which must be placed in the galvanometer
c rcuit in order that from an impressed E. M. F. of one volt there
s lall result a deflection of one millimeter" upon a scale one
r ieter from the reflecting mirror (Leeds and Northrup catalogue
2 ), 1918). The numerical value of this megohm sensitivity also
r ^presents the microampere sensitivity if this is defined as the
e imber of millimeters deflection caused by one microampere.

218 THE DETERMINATION OF HYDROGEN IONS

In hydrogen electrode measurements the resistance of the cells
varies greatly with design (length and width of liquid conductors)
and with the composition of the solutions used (e.g. saturated or
M/10 KC1). Constricted, long tubes may raise the resistance of
a chain so high as to annul the sensitivity of a galvanometer unless
this has a high megohm sensitivity. Dr. Klopsteg (private com-
munication) states that the resistance of the galvanometer coil
ideally should be of about the same order of magnitude as that
of the cell to be measured if maximum sensitivity is to be gained.
Here however we enter complexities, since the arrangements by
which high megohm sensitivity is attained affect other galva-
nometer characteristics. One of these, which is not essential but
is desirable, is a short period. A short period facilitates the set-
ting of a potentiometer. If the circuits are out of balance, as they
generally are at the beginning of a measurement, the direction for
readjustment may be inferred from the direction of galvanometer
deflection without bringing the coil back each time to zero setting,
but there comes a time when prompt return to zero setting is
essential to make sure that slight resettings of the potentiometer
are being made in the proper direction.

For a return of the coil to zero without oscillation it is neces-
sary to have some sort of damping. This is generally a shunt
across the galvanometer terminals, the so-called critical damping
resistance. This shunt permits a flow of current, when the main
galvanometer circuit is opened, which is generated by the turning
of the coil in the magnetic field. The magnetic field produced in
the coil by this current interacting with the field of the perman-
ent magnet tends to oppose the further swing of the coil. When
the resistance of the shunt is so adjusted to the galvanometer
characteristics that the swing progresses without undue delay to
zero setting and there stops without oscillation, the galvanometer
is said to be critically damped. Critical damping as applied to
deflection on a closed circuit need not be considered when the
galvanometer is used as a null point instrument. Since some of
the best galvanometers are not supplied with a damping resist-
ance the purchaser of an outfit for hydrogen electrode work should
take care to see that he includes the proper unit. Underdamped
and overdamped instruments will prove very troublesome or
useless.

THE POTENTIOMETER 219

These very brief considerations are presented merely as an aid
in the selection of instruments. The manner in which desirable
qualities are combined is a matter of considerable complexity but
fortunately makers are coming to appreciate the very simple but
important requirements for hydrogen electrode work and are
prepared to furnish them. The galvanometer now in use by the
author has the following characteristics; coil resistance 530 ohms,
critical damping resistance 9,000 ohms, period 6 seconds, sen-
sitivity 2245 megohms. It is not the ideal instrument for the
hydrogen electrode system in use but is satisfactory. A shorter
period is desirable and a higher coil resistance to correspond
better with the average resistance of the order of one to two
thousand ohms in some gas chains, would be desirable; but im-
provement in both of these directions at the same time may in-
crease the expense of the instrument beyond the practical worth.
Indeed certain instruments now on the market are satisfactory
for almost any type of hydrogen electrode measurements.

In using a galvanometer it is important to remember that while
the E. M. F. of a cell is unbalanced its circuit should be left closed
only long enough to show the direction of the galvanometer deflec-
tion. Otherwise current will flow in one direction or the other
through the chain and tend to upset the electrode equilibrium.
A mere tap on the key which closes the galvanometer circuit is
sufficient till balance is obtained.

Of potentiometer characteristics little need be said for the choice
in the first instance will lie between instruments sold by reliable
makers. In the second instance the choice will lie between
instruments of different range and many of the unique instruments
may be at once eliminated by a calculation which shows that the
reputed accuracy involves too close a scale reading to be reliable.
Certain difficulties which enter into the construction of potentio-
meters for accurate thermo-couple work are hardly significant
for the order of accuracy required of hydrogen electrode work.
The range from zero to 1.2 volts and the subdivisions 0.0001
volt do for measurements of ordinary accuracy. There should
be a variable resistance to accomodate the variations in individual
Weston cells of from 1.0175 to 1.0194 volts, and provision for
quickly and easily interchanging Weston cell with measured
E. M. F.

220 THE DETERMINATION OF HYDROGEN IONS

Several of the features of standard potentiometers may be elim-
inated without injury to their use for hydrogen electrode measure-
ments and would reduce their cost. Steps in this direction have
been taken by at least one manufacturer.

Having described the fundamental principles of the potentio-
meter it seems hardly worth while to discuss the numerous modi-
fications found among manufactured instruments or used in the
construction of home-made designs. With the advent into every
town of the numerous and varied parts of radio apparatus cer-
tain accessory parts of a potentiometer may be readily purchased
and the amateur can concentrate his attention upon the essential
resistances. But, unless he is equipped to make these with accur-
acy and to mount them with care, he may waste the cost of a
satisfactory instrument.

With regard to the more special or unique designs found on
the market it may simply be said that they were developed for
special purposes and that unless these special purposes are to be
accomodated, the purchaser will do well to depend only upon an
instrument of universal applicability.

When rubber is used as the insulating material of instruments
employed as potentiometers the rubber should not be left exposed
to the light unduly. The action of the light not only injures
the appearance of the rubber but also may cause the formation
of conducting surface layers.

If the potentiometer system contains a sliding contact and
this contact is not involved in the resistance of the primary poten-
tiometer circuit proper, the contact should be kept heavily coated
with pure vaseline. If there be any doubt whatever about the
quality of this vaseline it should be boiled with several changes
of distilled water, skimmed off when cool and then thoroughly
dried. If this is done there will seldom be any need to resort to
the heroic and dangerous procedure of polishing.

It cannot be too strongly emphasized that while a low order
of precision is often adequate for a certain purpose the employ-
ment of crude measuring instruments often obscures the data of
greatest significance. This statement should not be interpreted
as a discouragement to those who are about to undertake measure-
ments with some such system as that illustrated in figure 28 for
important data have been obtained with just such instruments.

THE POTENTIOMETER 221

The statement is intended rather as an encouragement to the
beginner who will find the handling of more precise instruments
easy and the rewards rich.

THE WESTON CELL

The elementary construction of the Weston cell is shown in
figure 33. The mercury in the left arm should be carefully puri-
fied (page 239) and the same material should be used for the
preparation of the cadmium amalgam. This amalgam consists
of 12.5 per cent by weight of electrolytic cadmium. The amal-
gam is formed by heating mercury over a steam bath and stirring
in the cadmium. Any oxid formed may be strained off by pouring
the molten amalgam through a test tube drawn out to a long
capillary.

Cadmium sulfate may be recrystallized as described by Wolff and
Waters (1907). Dissolve in excess of water at 70°C, filter, add
excess of basic cadmium sulfate and a few cubic centimeters of hy-
drogen peroxid to oxidize ferrous iron, and heat several hours.
Then filter, acidify slightly and evaporate to a small volume. Fil-
ter hot and wash the crystals with cold water. Recrystallize
slowly from an initially unsaturated solution. The cadmium sul-
fate solution of a "normal" Weston cell is a solution saturated at
whatever temperature the cell is used, and therefore the cell should
contain crystals of the sulfate. The ordinary unsaturated cell
has a cadmium sulfate solution that is saturated at about 4°C.

In the study of Weston cells considerable attention has been
paid to the quality of the mercurous sulfate. Perhaps the best
and at the same time the most conveniently prepared material is
that made electrolytically. Where the alternating current is
available it is preferable to use it. A good average set of condi-
tions is a sixty cycle alternating current sent through a 25 per cent
sulfuric acid solution with a current density at the electrodes of
5 to 10 amperes per square decimeter. With either the alternat-
ing or direct current the apparatus described on page 192 is
3onvenient.

In the Weston cell the lead-in wires of platinum should be
imalgamated electrolytically by making a wire the cathode in a
solution of pure mercurous nitrate in dilute nitric acid.

222

THE DETERMINATION OF HYDROGEN IONS

After filling the cell it may be sealed off in the blast flame or
corked and sealed with wax.

Since the preparation of a good Weston cell is a matter of con-
siderable detail, since such cells must be properly and carefully
made in order to establish the true potential differences in a poten-
tiometer system, and since reliable cells of certified values may be
purchased at a reasonable price, it hardly pays the individual
investigator to construct his own. It would, however, be a con-
venience if the materials could be purchased of the Bureau of
Standards as was once proposed.

In some portable Weston cells of commerce the mercury is
introduced as amalgamated electrodes and the cadmium sulfate
solution, instead of being always in the presence of cadmium
sulfate crystals, is often saturated at about 4°C. Since this leaves
the solution unsaturated at ordinary temperatures this cell is

Hgzso7

CdSO.

Hg-Cd

• Fig. 33. Diagram of the Weston Standard Cell

sometimes called the "unsaturated" type. The result is a cell
having a much lower temperature coefficient than that of the
"normal" cell. There remain, however, large, if opposite, tem-
perature coefficients for the two arms; and it is therefore necessary
to protect the cell from temperature changes which will affect
the two arms unequally. Furthermore in all Weston cells there
may be observed some degree of hysteresis and in particular
cases this may be very marked. It is therefore advisable under
all circumstances to protect any Weston cell from temperature
fluctuations.

Weston cells are standardized in terms of the international volt
the secondary standard for which is the average E. M. F. of

THE POTENTIOMETER

223

"normal" Weston cells maintained at each national standards
laboratory.

As the result of cooperative measurements by the national
standards laboratories of England, France, Germany and the
United States the value 1.01830 international volts at 20°C. was
assigned to the "normal" Weston cell. The United States Bu-
reau of Standards maintains a group of these normal Weston cells
whose mean value is taken as 1.0183 international volts and serves
for the standardization of the commercial cells. It is important
to note that this international agreement came into force January
1, 1911, and that prior to that time the values in force in different
countries varied considerably.

TABLE 44

TEMPERATURE

DIFFERENCE

°c.

+0.000,359

+0.000,366

+0.000,304

+0.000,179

0.000,000

-0.000,226

-0.000,492

-0.000,791

-0.001,114

The temperature coefficient of the "normal" Weston cell is
;iven by Wolff (1908) as:

Et = Esq - 0.000,040,75 (t - 20) - 0.000,000,944 (t - 20)2 +
0.000,000,009,8 (t - 20)3 (43)

3y this formula the differences in volts from the 20° value are as
;iven in table 44.

In other words a normal Weston cell should have its certified
/alue corrected by addition of the above corrections when used at
emperatures other than 20°C. But an "unsaturated" Weston cell
nay for all ordinary purposes be considered as having no tempera-
ure coefficient and its certified value may therefore be used as
; ;iven for all moderate variations from 20°C. The change in E. M.
<\ of the unsaturated type is less than 0.000,01 volt per degree,

224 THE DETERMINATION OF HYDROGEN IONS

provided the precautions regarding temperature fluctuations
previously mentioned are observed.

While most commercial cells are of the "unsaturated" type,
the purchaser should be informed whether a given cell is of the one
type or the other.

STORAGE BATTERIES

The storage battery or- accumulator is a convenient and reli-
able source of current for the potentiometer. Standard poten-
tiometers are generally designed for use with a single cell which
gives an E. M. F. of about two volts.

The more familiar cell to which our attention shall be confined
consists of two series of lead plates immersed in a sulfuric acid
solution of definite specific gravity. The plates of one series are
connected to one pole of the cell and the plates of the other series
are connected to the other pole. When a current is passed through
the cell it will produce lead peroxid upon the plates by which the
positive current enters and spongy lead upon the other plates. On
charging, therefore, the plates in connection with the positive pole
assume the brown color of the oxid while the plates in connection
with the negative pole assume the slate color of the spongy metal.
The poles should be distinctly marked so that one need not inspect
the plates to distinguish the polarity but should the marks become
obscured and the cell be a closed cell the polarity should be care-
fully tested with a voltmeter before attaching the charging cur-
rent. In lieu of a voltmeter the polarity may be tested with a
paper moistened with KI solution. On applying the terminals
to the paper a brown stain is produced at the positive pole, —
positive reaction at positive pole.

In charging a cell the positive pole of the charging circuit should
be connected to the positive terminal of the cell, else the cell will
be ruined. If a direct current lighting circuit is available, it may
be used to charge a cell, or battery of cells, provided sufficient
resistance be placed in series. A 16-candle-power carbon filament
on a 110-volt circuit allows about half an ampere to pass. A
bank of 6 lamps in parallel will allow three amperes to pass if
we neglect the battery resistance. Ordinarily one will do well
to charge at a rate lower than that specified by the maker, for the

THE POTENTIOMETER 225

care of a battery consists chiefly in keeping the deposits even.
Low rates of charge and discharge favor this. On charging, the
voltage will rise rapidly to 2.35 volts where it will remain during
the greater part of the period. When it rises to 2.5 volts the
charging should be discontinued. It is when it has reached this
voltage that the cell will "gas" vigorously. If a cell should fail
to "gas" after a reasonable time it may have an internal short
circuit due to warping of the plates or the scaling of conducting
material. In searching for such a condition a wooden pry, never
a metallic one, should be used. Careful handling and charging
will generally prevent such short circuits.

It is more economical to charge from a low voltage circuit but
this is seldom available. Indeed there is often available only an
alternating current of lighting-circuit voltage. To use the energy
of an alternating current it must either be used with a motor
generator furnishing a direct current (preferably of low voltage)
or else rectified. There are now readily available a variety of
rectifiers used in charging the batteries of radio amateurs. Most
of these rectifiers when of the mechanical type are designed for
charging a six-volt battery. If the operator of a hydrogen elec-
trode has a two-volt cell for his potentiometer and a four-volt
battery for operating the relay of the temperature control sys-
tem he has a combination suited to the common and inexpensive
type of rectifier.

In the discharging of a cell the sulfuric acid is converted to sul-
fate which is deposited. The result is the lowering of the specific
gravity of the battery liquid. Thus the specific gravity of the
liquid is highest when the battery is fully charged and lowers on
discharging. If there be reason to suspect that the proper spe-
cific gravity is not being maintained it should be measured with
i hydrometer. Fresh sulfuric acid may be added if one follows
carefully the specifications given by the manufacturer of the cell,
'n making fresh solution only sulfuric acid free from metals other
han lead, free from arsenic, and free from chloride and nitrate
hould be used. There will be a continuous loss of water from the
>attery liquid due to evaporation and gassing. This should be
eplaced by distilled water during the recharging of the cell.

In discharging a cell its voltage should not be allowed to fall
1 elow 1.8 volts. When a cell has reached this voltage it should be

226 THE DETERMINATION OF HYDROGEN IONS

recharged immediately. If however the cell has been discharged
to a lower voltage it should be recharged at half rate.

In using a storage cell to supply potentiometer current it is es-
sential that the highest stability in the current should be attained
since the fundamental principle of the potentiometer involves the
maintenance of constant current between the moment at which
the Weston cell is balanced and the moment at which the measured
E. M. F. is balanced. Steadiness of current is attained first by
having a storage cell of sufficient capacity, and second by using it
at the most favorable voltage. Capacity is attained by the num-
ber and size of the plates. A cell of 60 ampere-hour capacity is
sufficient for ordinary work. The current from a storage cell is
steadiest when the voltage has fallen to 2 volts. When a potenti-
ometer system of sufficient resistance is used it is good practice to
leave the cell in circuit, replacing it or recharging it of course when
the voltage has fallen to 1.8 or 1.9 volts, and thus insure the at-
tainment of a steady current when measurements are to be made.

In no case should a cell used for supplying potentiometer cur-
rent be wired so that a throw of a switch will replace the discharg-
ing with the charging circuit. The danger of leakage from the
high potential circuit is too great a risk for the slight convenience.

CHAPTER XV

Hydrogen Generators, Wiring, Shielding, Temperature
Control, Purification of Mercury

Hydrogen generators. When there is no particular reason for
attaining equilibrium rapidly at the electrode a moderate supply
of hydrogen will do. When, however, speed is essential, or
when there are used those immersion electrodes which are not
well guarded against access of atmospheric oxygen an abundant
supply of hydrogen is essential. Indeed it may be said that
one of the most frequent faults of the cruder equipments is the
failure to provide an adequate supply of pure hydrogen or the
failure to use generously the available supply.

Hydrogen generated from zinc and sulfuric acid has been used

n a number of investigations. If this method be employed,

particular care should be taken to eliminate from the generator

;hose dead spaces which are frequently made the more obvious

evidence of bad design, to have an abundant capacity with which

o sweep out the gas spaces of cumbersome absorption vessels

. md to properly purify the hydrogen. To purify hydrogen made

irom zinc and sulphuric acid pass it in succession through KOH

l olution, HgCl2 solution, P2O5, red-hot, platinized asbestos, and a

solution of Na2S204 (See Franzen, Ber., 39, 906) (Henrich, Ber.,

k 8, 1915, p. 2006).

A very convenient supply of hydrogen is the commercial,
( ompressed gas in tanks. According to Moser (1920) the indus-
t rial preparation varies but the chief methods are the electrolytic
1 nd the Linde-Cara-Franck processes. Of these the first yields
t le better product. Hydrogen by the second process contains
s tnong other impurities, iron carbonyl which may be detected by
t le yellow flame and the deposit of iron oxid formed when the
r ydrogen flame impinges upon cold porcelain. Moser found that
i' was impractical to remove this iron carbonyl and he states that
h ydrogen containing it is unfit for laboratory purposes. On the
0 ;her hand, electrolytic hydrogen ordinarily contains only traces
0 air and C02 and is free from arsenic and CO. To purify it

227

228 THE DETERMINATION OF HYDROGEN IONS

pass the gas over KOH and then through a tube of red-hot, platin-
ized asbestos. If it is desired to dry the hydrogen, use soda lime
or P2O5, but not H2SO4 which is reduced. If P20B is used it should
be free from P2O3, i.e., distilled in a current of hot dry air.

In purchasing tank hydrogen it is well to be on guard against
tanks which have been used for other gases.

For controlling the flow of gas from a high pressure tank the
valve on the tank itself is seldom sufficiently delicate. There
should be coupled to it a delicate needle valve, if this can be
obtained. If not there will be found on the market diaphragm
valves for the reduction of the pressure. Even then there should
be placed between the tank and the electrode vessel a T tube, one
branch of which dips under mercury and forms a safety valve.

Having metal connections to start with, it will be found very
satisfactory to lead off with copper tubing, such as is used for
automobile connections or specified as soft drawn, seamless copper
tubing 4 mm. internal diameter and wall thickness 24 B. S. gauge.
This can be soldered in the flame of a blast lamp, using borax for
a flux, with a silver solder composed of 6.5 parts copper, 2.0
parts zinc and 11.0 parts silver. This solder is described as fus-
ing at about 983°C. A nickel wire is useful in spreading the
flux and solder.

On the whole electrolytic generators are more satisfactory if
a direct current such as that of a lighting circuit is available.
In figure 34 is shown a generator the body of which is an ordinary
museum jar. The glass cover may be perforated by drilling with
a brass tube fed with a mixture of carborundum and glycerine. If
this mixture is kept in place by a ring paraffined in position, and
the brass tube is turned on a drill press with intermittent
contact of the drill with the glass, the perforation may be .made
within a few minutes. The electrolyte used is ten per cent,
sodium hydroxid. The electrodes are nickel. To remove
the spatter of electrolyte and to protect the material in the heater
the hydrogen passes over a layer of concentrated KOH solution;
and to remove traces of residual oxygen the hydrogen is passed
through a heater. In the design shown the gas passes through a
tungsten filament lamp. Lewis, Brighton and Sebastian use a
heated platinum wire. More commonly there is used a gas-heated
or electrically heated tube containing platinized asbestos. In

HYDROGEN GENERATORS, ETC.

229

the author's design shown in figure 34 the wiring is so arranged
that when there is no demand for hydrogen the heater may be
turned off at S2 and a lamp thrown into series with the generating

- +
I

Fig. 34. An Electrolytic Hydrogen Generator

circuit by switch Si. The generator then continues to operate
on a low current and sufficient hydrogen is liberated to keep the
system free from air. Such a generator can be run continuously
for months at a time. When in use the generator carries about

230 THE DETERMINATION OF HYDROGEN IONS

4.5 amperes. If this current be taken from a high voltage light-
ing system there must be placed in series a proper resistance which
can be either built up by a bank of lamps or constructed from
nichrome wire.

Since rubber connections are often used in leading hydrogen
it is of interest to note the following relative rates of diffusion of
gases through rubber.

Gab Rate

Nitrogen 1.00

Air 1.15

Oxygen 2.56

Hydrogen 5.50

Carbon dioxid 13 .57

Wiring. Whenever a set-up is to be made more than an improv-
isation it pays to make a good job of the wiring. A poor connec-
tion may be a source of endless trouble and unsystematized wiring
may lead to confusion in the comparison of. calomel electrodes
and the application of corrections of wrong sign.

Soldered connections or stout binding posts that permit strong
pressure without cutting of the wire are preferable to any other
form of contact. If for any reason mercury contacts are used
they had best be through platinum soldered to the copper lead.
Copper wires led into mercury should not take the form of a
siphon else some months after installation it may be found that
the mercury has been siphoned off.

Thermo-electromotive forces are seldom large enough to affect
measurements of the order of accuracy with which we are now
concerned if care be taken to make contacts so far as possible
between copper and copper at points subject to fluctuations in
temperature.

A generous use of copper knife switches, can be made to con-
tribute to the ease and certainty of check measurements. For
instance if there be a battery of hydrogen electrodes and a set of
calomel electrodes, wires may be led from each to a centre con-
nection of single-pole, double-throw switches as shown in figure 35.
All the upper connections of these switches are connected to the
+ pole of the potentiometer's E. M. F. circuit, and all the lower
connections to the — pole. By observing the rule that no two
switches shall be closed in the same direction, short-circuiting of

HYDROGEN GENERATORS, ETC.

231

combinations is avoided. The position of a switch shows at once
the sign of its electrode in relation to any other that may be put
into liquid junction. This is a great convenience in comparing
calomel electrodes where one half-cell may be positive to another
and negative to a third. Such a bank of single pole switches per-
mits the comparison of any electrode with any other when liquid
junction is established; and, if a leak occur in the electrical sys-
tem the ability to connect one wire at a time with the potenti-
ometer and galvanometer often helps in the tracing of the leak.

Fig. 35. Switches for Connecting Half-Cells with Potentiometer

Shielding. Electrical leaks from surrounding high potential cir-
cuits are sometimes strangely absent from the most crude systems
and sometimes persistently disconcerting if there is not efficient
shielding. The principle of shielding is based on the following
considerations. If between two supposedly well-insulated points
on a light or heating circuit, or between one point of such a circuit
and a grounding such as a water or drain pipe, there is a slight
flow of current, the electrical charges will distribute themselves
over the surface films of moisture on wood and glass-ware. At
two points between which there is a difference of potential the wires
of the measured or measuring system may pick up the difference of
potential to the detriment of the measurement. If however all
supports of the measured and measuring systems lie on a good con-
ductor such as a sheet of metal, the electrical leakage from without

232 THE DETERMINATION OP HYDROGEN IONS

will distribute itself over an equipotential surface and no differ-
ences of potential can be picked up. To shield efficiently, then,
it is necessary that all parts of the system be mounted upon metal
that can be brought into good conducting contact. In many in-
stances the complications of hydrogen electrode apparatus and
especially the separation of potentiometer from temperature bath
make a simple shielding impracticable. Care must then be taken
that all of the separate parts are well connected. Tinfoil winding
of wire in contact with unshielded points can be soldered to stout
wires for connection to other parts by dropping hot solder on the
well-cleaned juncture.

Shielding should not be considered as in any way taking the
place of good insulation of the constituent parts of the measured
or measuring systems.

For further details in regard to shielding see W. P. White (1914).

Temperature control is" a matter where individual preference holds
sway. There are almost as many modifications of various types
of regulators as there are workers. Even in the case of electrical
measurements where orthodoxy interdicts the use of a water bath
it has been said (Fales and Vosburgh) that it can be made to give
satisfaction.

Yet there are a few who may actually make use of a few words of
suggestion regarding temperature control for hydrogen electrode
work.

As a rule the water bath is not used because of the difficulty of
preventing electrical leakage. Some special grades of kerosene are
sold to replace the water of an ordinary liquid bath but for most
purposes ordinary kerosene does very well. The free acid some-
times found in ordinary kerosene may injure fine metallic instru-
ments. To avoid this use the grade sold as " acid-free, medium,
government oil."

A liquid bath has the advantage that the relatively high spe-
cific heat of the liquid facilitates heat exchange and brings material
rapidly to the controlled temperature, but compared with an air
bath it has the disadvantage that stopcocks must be brought up out
of the liquid to prevent the seepage of the oil. The advantage of
the high specific heat of a liquid is falsely applied when the con-
stancy of a liquid bath is considered to be a great advantage over
the more inconstant air bath. The lower the specific heat of the

HYDROGEN GENERATORS, ETC. 233

fluid the less effect will variation in the temperature of that fluid
have upon material which it is desired to keep at constant tem-
perature. For this reason a well-stirred air bath whose tempera-
ture may oscillate about a well-controlled mean may actually
maintain a steadier temperature in the material under observa-
tion than does a liquid bath which itself is more constant. It is
the temperature of the material under observation and not the
temperature of the bath which is of prime interest.

An air bath can be made to give very good temperature control
and since it is more cleanly than an oil bath and permits direct-
ness and simplicity in the design of apparatus a brief description
of one form used by the writer for some years may be of interest.

A schematic longitudinal section illustrating the main features
is shown in figure 36.

The walls of the box are lined with cork board finished off on
the interior with "compo board." The front is a hinged door
constructed like the rest of the box but provided with a double
glass window and three 4-inch hand holes through which appara-
tus can be reached. On the interior are mounted the two shelves
A and B extending from the front to the back wall and providing
two flues for the air currents generated by the fan F.

The writer at one time used a no. 0 Sirocco fan manufactured
by the American Blower Company, demounted from its casing
and mounted in the bearing illustrated. He now uses a four-
blade fan taken from a desk-fan and mounted so that it turns
in the hole F of the partition and blows toward E. The baffle
plates at E, made of strips of tin arranged as in an egg-box,
and intended to establish parallel lines of flow when the centri-
fugal fan was used, are now eliminated.

In the illustration the oil cup is shown as if it delivers into an
annular space cut out of the Babbit-metal bearing. In reality
this annular space is provided by cutting away a portion of the
steel shaft.

The heating of the air is done electrically with the use of bare,
aichrome wire of no. 30 B. and S. gauge. When using the centrif-
ugal fan the wire is strung between rings of absestos board (the
'lard variety known as "transite" or " asbestos wood") which fit
:>ver the fan at H. With the blade-fan the partition at F is made
)f asbestos board and the wire is strung over the opening. The

234

THE DETERMINATION OF HYDROGEN IONS

air is thus heated at its position of highest velocity. The elec-
trical current in this heating coil can be adjusted with the weather
so that the time during which the regulator leaves the heat on is
about as long as the time during which the regulator leaves the
heat off. In other words adjustment is made so that the heating
and cooling curves have about the same slope, or so that the heat-
ing balances the loss of heat through the walls.

1 FOOT

t- i — r—\ — i — i i i i i

— *—"

-:— \

Fig. 36. Cross Section of an Air Bath

When the room temperature is not low enough to provide the
necessary cooling the box I is filled with ice water. Surrounding
this is an air chamber into which air is forced from the high pres-
sure side of the fan. J should be provided with a damper which
can easily be reached and adjusted.

To lessen danger of electrical leakage over damp surfaces the
air is kept dry by a pan of calcium chlorid.

A double window at W over which is hung an electric light pro-
vides illumination of the interior. A solution of a nickel salt is
placed at this window to absorb the heat from the lamp.

HYDROGEN GENERATORS, ETC. 235

The double window in the door (not shown) should be beveled
toward the interior to widen the range of vision.

Such a box has been held for a period of eight hours with no
change which could be detected by means of a tapped Beckmann
thermometer and with momentary fluctuations of 0.003° as de-
termined with a thermo-element. The average operation is a
temperature control within ±0.03° with occasional unexplained
variations which may reach 0.1°. Because of the slowness with
which air brings material to its temperature the air bath is con-
tinuously kept in operation, and if a measurement is to be made
quickly the solution is preheated.

Given efficient stirring and a considerate regulation of the
current used in heating, accurate temperature control reduces to
the careful construction of the regulator. For an air bath the
ideal regulator should respond instantaneously. This implies
rapid heat conduction. Regulators which provide this by having
a metal container have been described but glass will ordinarily be
used. At all events there are two simple principles of regulator
construction the neglect of which may cause trouble or decrease
sensitivity and attention to which improves greatly almost any
type. The first is the protection of the mercury contact from the
corroding effect of oxygen. The second is the elimination of plati-
num contacts which mercury will sooner or later "wet," and the
substitution of an iron, nickel or nichrome wire contact.

After trials of various designs the author has adopted the two
forms of regulator head shown in figure 37.

For precise control at an inaccurately adjusted temperature
form A is used. The platinum lead-in wire P is fused to the ni-
chrome wire N. After filling the instrument with mercury, dry
hydrogen is flushed through the head by way of the side tubes.
These are then sealed off and serve as reservoirs for excess mer-
cury. Adjustment is made by slightly overheating the body of
the mercury, breaking off the capillary column by a tap of the
hand and storing the detached portion in one of the side tubes.
Such an adjustment is often troublesome when regulation at a
particular temperature is desired; but, once the adjustment is made
it is permanent, provided the contact wire is ground down to a
fine thread so that it will not fill the capillary enough to cause the
mercury thread to part on occasions of overheating.

236

THE DETERMINATION OF HYDROGEN IONS

Form B permits delicate adjustment of the contact by means of
the screw S but it requires skill to make such a head properly.
The nichrome wire must fit very closely in the capillary R to pre-
vent the wax and mercury seal at W from creeping downward.
Such a close fit implies very careful glass blowing to maintain a

Fig. 37. Thermo-Regtjlator Heads

straight and unconstricted capillary. With the contact wire in
place and the proper amount of mercury in the apparatus hydrogen
is run in at T escaping through R. Then a bit of beeswax is
melted about W and at the moment it hardens the hydrogen sup-
ply is shut off, T is sealed, and then the wax is covered with a
shallow layer of mercury.

HYDROGEN GENERATORS, ETC. 237

If the wire does not fit R with precision or if overheating occurs
the mercury at W may find its way into the regulator head. It
is much safer then, although it increases the difficulties of adjust-
ment, to make the seal at W with DeKhotinsky cement.

For an air bath it is best to seal such regulator heads to a
grid of tubes.

The permanency of regulators of such design when properly
made is a great asset and well repays care in preparation. Regu-
lators of each of these types have been in continuous operation for
years without serious trouble. One of type A survived a severe
laboratory fire and after readjustment operated well.

Filling such regulators with mercury can be done most easily
by first evacuating the vessel under some one of the various high
vacuum pumps and then letting the mercury in slowly through one
of the side arms drawn to a fine point which is. broken under
mercury.

A description of methods of purifying mercury will be found on
page 239.

For electrical control of temperature the scheme of wiring
shown in figure 38 has proved satisfactory.

Lamps which are neat, convenient, replacable forms of resist-
ance, which are obtainable in variety and which indicate whether
or not current is flowing are shown in figure 38 "by L. R is a
resistance formed by a few turns of number 30 nichrome wire on
Pyrex glass, porcelain or asbestos board. By shifting the brass
contact clamp along this resistance the proper amount of cur-
rent to operate the relay may be found by trial. Too strong a
current is to be avoided. A sharp, positive action of the relay
should be provided against the day when the relay contact may
become clogged with dust. To reduce sparking at the regulator
and at the relay contacts, inductive coils in the wiring should be
avoided. Spanning the spark gaps with properly adjusted con-
densers made of alternate layers of tin foil and paraffine paper
may eliminate most of the sparking, if the proper capacity be
used. For air regulation it is essential that the heater be of
bare wire so that it cools the moment the current is turned off.
Furthermore it is essential to adjust the current till the heating
rate is close to the cooling rate of the air bath. For such control
of the heating current there are inserted in series with the heater

238

THE DETERMINATION OF HYDROGEN IONS

two lamp sockets in parallel permitting the insertion of either a
fuse, one lamp or two lamps of various sizes. The other lamp
shown in the heating circuit reduces sparking at the relay.

For relay contacts the tungsten contacts used in gas engines
are very good.

Although methods of tapping an alternating current for the
operation of a relay have been described it is safer to depend upon
a battery.

To
VUa-YtY

Fig. 38. Wibing for Temperature Control

Purification of mercury. Pure mercury is essential for many
purposes in hydrogen electrode work, — for the calomel and the
mercury of calomel electrodes, for Weston cells should these be
"home made," for thermo-regulators and for the capillary elec-
trometer.

The more commonly practiced methods of purification make use
of the wide difference between mercury and its more troublesome
impurities in what may be descriptively put as the "electrolytic
solution tension." Exposed to any solution which tends to dis-
solve base metals the mercury will give up its basic impurities

HYDROGEN GENERATORS, ETC. 239

before it goes into solution itself, provided of course the reaction
is not too violent for the holding of equilibrium conditions.

The most commonly used solvent for this purpose is slightly
diluted nitric acid' although a variety of other solutions such as
that of ferric iron may be used.

To make such operations efficient it is necessary to expose as
large a surface as possible to the solution. Therefore the mercury
is sometimes sprayed into a long column of solution which is sup-
ported by a narrow U-tube of mercury. The mercury as it col-
lects in this U-tube separates from the solution and runs out into
a receiver. To insure good separation the collecting tube should
be widened where the mercury collects but this widening should
not be so large as to prevent circulation of all the mercury. A
piece of very fine-meshed silk tied over the widened tip of a funnel
makes a fine spray if the silk be kept under the liquid. This sim-
ple device can be made free from dead spaces so that all the mer-
cury will pass through successive treatments. It is more difficult
to eliminate these dead spaces in elaborate apparatus; but such
apparatus, in which use is made of an air lift for circulating the
mercury, makes practicable a large number of treatments. A
combination of the air lift with other processes and. a review of
similar methods has been described by Patten and Mains (1917).

Hulett's (1905, 1911) method for the purification of mercury
consists in distilling the mercury under diminished pressure in a
current of air, the air oxidizing the base' metals. Any of these
oxids which are carried over are filtered from the mercury by pass-
ing it through a series of perforated filter papers or long fine cap-
illaries. A convenient still for the purpose is made as follows.
Fuse to the neck of a Pyrex Kjeldahl flask a tube about 30cm. long
which raises out of the heat of the furnace the stopper that car-
ries the capillary air-feed. Into the neck of the flask fuse by a T-
joint seal a 1.5 cm. tube and bend this slightly upward for a
length of 15 cm. so that spattered mercury may run back. To the
end of this 15 cm. length join the condensing tube, which is simply
an air condenser made of a meter length of narrow tubing bent
zigzag. Pass the end of this through the stopper of a suc-
tion flask and attach suction to the side tube of this flask. The
mercury in the Kjeldahl flask may be heated by a gas flame or an
electric furnace. For a 220 volt D. C. circuit 12 meters of no. 26

240 THE DETERMINATION OF HYDROGEN IONS

nichrome wire wound around a thin asbestos covering of a tin
can makes a good improvised heating unit if well insulated with
asbestos or alundum cement. A little of this cement applied
between the turns of wire after winding will keep the wire in place
after the expansion by the heat.

In the construction of such stills it is best to avoid soft glass
because of the danger of collapse on accidental over-heating.
Hostetter and Sosman describe a quartz still.

Both the air current, that is delivered under the surface of the
mercury by means of a capillary tube, and the heating should be
regulated so that distillation takes place smoothly.

Since it is very difficult to remove the last traces of oxid from
mercury prepared by Hulett's distillation the author always makes
a final distillation in vacuo at low temperature. An old but good
form of vacuum still is easily constructed by dropping from the
ends of an inclined tube two capillary tubes somewhat over baro-
metric length. One of these is turned up to join a mercury res-
ervoir, the other, the condenser and delivery tube, is turned up
about 4 inches to prevent loss of the mercury column with changes
in external pressure. The apparatus is filled with mercury by suc-
tion while it is inclined to the vertical. Releasing the suction and
bringing the still to the vertical leaves the mercury in the still
chamber supported by a column of mercury resting on atmospheric
pressure and protected by the column in the capillary condenser.
The heating unit is wire wound over asbestos. The heat should
be regulated by a rheostat till the mercury distills very slowly.
By having the mercury condense in a capillary the still becomes
self-pumping.

Perhaps few of us who work with mercury have a proper regard
for the real sources of danger to health. The vapor pressure of
mercury at laboratory temperatures is not to be feared, but emul-
sification with the dust of the floor may subdivide the mercury
until it can float in the air as a distinct menace. Its handling
with fingers greasy with stop cock lubricant is also to be avoided
on account of possible penetration of the skin but more particu-
larly because of the demonstrated ease with which material on
the hands reaches the mouth.

HYDROGEN GENERATORS, ETC. 241

REFERENCES

Potentiometers

Bartell (1917), Bovie (1915), Hildebrand (1913), Leeds and Northrup Cata-
logue 70, McClendon (1915), Nye (1921), Sand-Law (1911), Slagle-
Acree (1921), Wenner-Weibel (1914), White (1914), Will Corporation
(1921).

Galvanometers

Leeds and Northrup Company Catalogue 20 (1918), White (1906).

Capillary electrometer

Boley (1902), Le Blanc (1890), Lippmann, G. (1875), Smith (1900) (1903).

Quadrant electrometer

Beattie (1910-12), Compton-Compton (1919), Dolezalek (1906).

Weston standard cell

Bureau Standards Circular 60, Report to International Committee (1912),
Cohen-Moesveld (1920), Cohen-Walters (1920), Wolff (1908), Wolff-
Waters (1907), Hulett (1906), Melon (1921), Oblata (1920).

International electrical units
Dellinger (1916), Bureau Standards Circulars Nos. 29, 60.

CHAPTER XVI

The Relation of Hydrogen Electrode Potentials to
Reduction Potentials

We must remember that we cannot get more out of the mathematical
mill than we put into it, though we may get it in a form infinitely more
useful for our purpose. — John Hopkinson

As indicated in Chapter X the hydrogen electrode is but a
special case of a general relation for the potential difference be-
tween a metal and a solution. The hydrogen electrode is con-
structed of a noble metal laden with hydrogen, and it may be
asked what relation it bears to those electrodes which consist of
the noble metal alone and which are used to determine the so-
called oxidation-reduction potentials of solutions such as mix-
tures of ferrous and ferric iron.

If a platinum or gold electrode be placed in a mixture of fer-
rous and ferric sulfate there will almost immediately be assumed
a stable potential difference which is determined by the ratio
of the ferrous to the ferric ions. The relation which is found to
hold is given by the equation:

fc-fc-MfcEsd (44)

nF [Fern]

where Eh is the observed potential difference between the elec-
trode and the standard normal hydrogen electrode, E^ is a con-
stant characteristic of this particular oxidation-reduction equilib-

[Ferro]
rium and equal to Eh when the ratio — — jj is unity, R, T, n

and F have their customary significances, and [Ferroj and [Ferri]
represent concentrations of the ferrous and the ferric ions re-
spectively. This equation will be referred to later as Peters'
equation. Its general form is:

RT, [RED] , %

where [RED] represents the concentration of the reductant and
[OX] represents the concentration of the oxidant.

242

REDUCTION POTENTIALS 243

If we plot Eh on one coordinate and the percentage reduction
on the other coordinate, we obtain a set of curves identical in
form for a given value of n. The position of each curve along
the Eh axis is determined by the value of Ek which fixes the middle
point. Such a set of curves would present a picture comparable
with that shown in figure 2. The picture, however, would be
incomplete for reasons which will be given later.

It will be clearly understood that in using the term oxidation
or the term oxidant we do not imply that oxygen is concerned.
Oxidation is one of those terms established under an old order
of thought and carried on into a new order with its meaning
broadened. In the transformation of ferrous to ferric iron by
chlorine there is every reason to believe that the process is directly
one of electron transfer; yet we speak of it as an "oxidation"
because it was seen fit at one time to systematize such reactions
in terms of the participation of oxygen. The counterpart of
oxidation is reduction. This term does not directly indicate any
relation to hydrogen, but it is often assumed that hydrogen is
concerned in reduction in much the same way that oxygen was
thought to be concerned in every "oxidation."

Before coming to a more generalized theory we shall describe
the relation between the hydrogen electrode and the oxidation-
reduction electrode in terms of hydrogen and hydrogen ions. .

It is known that certain reducing agents are so active that
they evolve hydrogen from aqueous solutions. In such a solu-
tion an electrode would become charged with hydrogen and
would conduct itself much like a hydrogen electrode. The relations
then obtaining can be extended and, if we wish to represent the
interaction of the reducing agent with the hydrogen ions, we have:

H+ + reducing agent ^ H + oxidation product.

If equilibrium is established for the above reaction

[H+] [RED] =
[H] [OX]

[H] _ [RED]

FH+] [OX]

244 THE DETERMINATION OF HYDROGEN IONS

[H] [RED]

Substituting K zz^;, for the ratio "77^77 in Peters' equation

(45) and placing n = 1 for the case at hand we have

Since the atomic hydrogen bears a definite relation to the partial
pressure of molecular hydrogen, P, through the equilibrium

[Hj2 = KhP

we mav substitute, collect constants under another constant K',
bring this under Ek and so obtain:

- „, RT. \/~P~ , N

Eh = Ek - — In _ .(46)

Compare this with the general relation for the hydrogen electrode

„ „ RT. V^P~ , %

Eh = EH In — — (47)

F [H+]

EH in (47) is zero by definition when there is used the "normal
hydrogen electrode" system of reference. When (46) is placed
on .the same basis Ek is also zero, since each of the other terms in

(46) is identical with the corresponding term in (47).

In other words we have substituted for the oxidation-reduction
equilibrium the corresponding point of equilibrium between
hydrogen and hydrogen ions, and have considered the poten-
tial difference at the electrode as if it were that of a hydrogen
electrode. An inference is that wherever we have an oxidation-
reduction equilibrium the components will interact with hydrogen
ions (or water) liberating free hydrogen and building up in the
electrode a definite pressure of hydrogen. Conversely, if hydro-
gen is already present in the electrode at a pressure too high for
the oxidation-reduction equilibrium in question, hydrogen will
be withdrawn until its pressure is in harmony with the oxidation-
reduction equilibrium (the position of the latter having been
shifted more or less by the reduction) . When a constant pressure
of hydrogen is maintained at the electrode, as it is in the customary
use of the hydrogen electrode, no true equilibrium can be attained

REDUCTION POTENTIALS 245

until this hydrogen has so far reduced all the substances in
the solution that they can support one atmosphere pressure of
hvdrogen.

Incidentally it may be mentioned that it is a matter of indiffer-
ence whether we regard the reductant to interact with the hydro-
gen ions or the oxidant with the hydroxyl ions or each with water.
By use of the equilibrium equations which are involved we reach
the same end-result whatever the path. And furthermore by
the use of certain theoretical relations between the hydrogen elec-
trode and the oxygen electrode we could define potential differences
in terms of that of an oxygen electrode.

This method of relating oxidation-reduction to electrode poten-
tials is convenient for showing the condition which must obtain for
a true hydrogen electrode potential; but when we attempt to
follow some of the logical consequences of this, the customary
exposition, we not only meet some serious difficulties but obscure
some very important relations.

Let us calculate the hydrogen pressure in equilibrium with an
equimolecular mixture of ferrous and ferric chlorid in a solution
held at pH 1. A platinum electrode in such a solution will have
a potential about 0.75 volt more positive than the "normal hy-
drogen electrode." Let us consider this to be the difference of
potential between a hydrogen electrode at pH 1 and a normal
hydrogen electrode. Let us calculate, then, the hydrogen pressure
at 25°C. from the equation:

0.75 = - 0.0599 log —
0.1

We find the hydrogen pressure to be about 10~27 atmospheres.
At one atmosphere pressure a gram mol of hydrogen occupies
about 22 litres and contains about 6 X 1023 molecules. If the
pressure is reduced to 6 X 10-23 atmospheres there would be but
one molecule of hydrogen in 22 litres. If reduced to 10-27 at-
mospheres there would be but one molecule in about 37,000 litres.
To assume any physical significance in such values is, of course,
ridiculous.

It is only by courtesy then that an electrode in a mixture of
ferrous and ferric iron at pH 1 can be considered as a hydrogen
electrode.

246 THE DETERMINATION OF HYDROGEN IONS

This is but an instance of the physically absurd values encoun-
tered when restricted points of view and restricted methods of expressing
relations are applied to electrode potential differences. One or two
other instances will be given to illustrate the fact that our
present equations are incomplete in that they tell us little or
nothing about the mechanisms at electrodes (see Langmuir 1916,
also Smits and Aten 1916).

Lehfeldt (1899) says of the so-called solution pressures postu-
lated by Nernst and briefly discussed in Chapter X:

we have Zinc 9.9 X 1018

Nickel 1.3 X 10°

Palladium 1.5 X 10~36

The first of them is startlingly large. The third is so small as to involve
the rejection of the entire molecular theory of fluids.

Lehfeldt then shows that, in order to permit at the electrode
the pressure indicated above for palladium, the solution would
have to be so dilute as to contain but one or two ions of palladium
in a space the size of the earth. No stable equiHbrium could be
measured under such a circumstance. On the other hand Leh-
feldt calculates that to produce the high pressure indicated for
zinc "1.27 grams of the metal would have to pass into the ionic
form per square centimeter, which is obviously not the case."
There is thus very good reason to refrain from attributing a limited
and sometimes obviously untrue physical significance to the in-
tegration constant in the fundamental equation for electrode
potentials (see page 153).

Another aspect of the matter was emphasized in a lively dis-
cussion between Haber, Danneel, Bodlander and Abegg in Zeit-
schrift fur Elektrochemie, 1904. Haber points out that, if the
well established relation between silver ion concentration and the
potential difference between a silver electrode and a solution
containing silver ions be extrapolated to include the conditions
found in a silver cyanide solution, the indicated concentration of
the silver ion will be so low as to have no physical significance.
Haber mentions the experiment of Bodlander and Eberlein where
the potential and the quantity of solution were such that there
was present at any moment less than one discrete silver ion. The
greater part of the discussion centred upon the resolution of the
equilibrium constant into a ratio of rates of reaction, and upon

REDUCTION POTENTIALS 247

the' conclusion that, if the silver ion in the cyanide solution has a
concentration of the order of magnitude calculated, it must react
with a speed greater than that of light or else that the known reac-
tions of silver in cyanide solutions must take place partly with
the silver complexes and not wholly with the silver ions. How-
ever, we are now more directly concerned with another aspect of
this interesting situation. The potentials observed in silver cya-
nide solutions are well defined. We may choose to extend to
such solutions the relation between the potential of a silver elec-
trode and silver ion concentration. When we do, we find that the
silver ion concentration by itself cannot account for the well-de-
fined potential. How then is the stable and reproducible poten-
tial supported?

None of these discussions affect in any serious way those rela-
tions for concentration chains which are founded upon thermo-
dynamic reasoning provided it be remembered that the thermo-
dynamic reasoning alone does not furnish any conception of the
physical mechanisms of a process. The points mentioned do how-
ever make it evident that values sometimes used are mere "cal-
culation numbers" employed in a region of extrapolation where
the actual physical significance is unknown. The inevitable con-
clusion is that our equations are insufficiently generalized.

Such "calculation numbers" as those mentioned in the pre-
3eding discussion are often of very great usefulness, but lest
ihey continue to obscure phenomena of significance we shall
soon have to have equations more intimately related to the mech-
misms as Langmuir pointed out in his 1916 paper.

Now it will not remove the fundamental difficulty to use the

reatment which follows; but this treatment may aid the student

o retain an orderly view of important relations, and it will pro-

" 'ide a basis from which to discuss the interrelations of electrodes

<f different types. From this discussion a generalized point of

" iew will be reached.

It is generally agreed that the fundamental process in oxida-
1 on-reduction is an exchange of electrons. A familiar example is:

Ferric ion + electron ^=± ferrous ion

Fe+++ + e ?± Fe++

Since such a reversible reaction is not dependent upon the
F 'esence of an electrode (acting as a catalyst) it is probable that

248 THE DETERMINATION OF HYDROGEN IONS

an exchange of electrons is going on continuously. There must
then be some condition virtually equivalent to a free-electron
pressure. We may imagine a moment in the exchange during
which the electron is balanced between the forces of each ion.
At this moment the electron may be considered to belong to
neither ion and to be a property of the environment. Undoubtedly
the situation is not so simple as this picture suggests; and, al-
though the presence of free electrons has been demonstrated in
liquid ammonia and methylamine solutions, the experimental
evidence is not sufficient to justify our assuming the presence of
free electrons in aqueous solutions to be a fact. However, it may
be said at once that we are not now concerned with the objective
actuality. A pressure of free electrons is merely postulated as
the virtual equivalent of a condition not yet clearly formulated;
and it is to be used in much the same way that Nernst used "so-
lution tension," destined from the first to be eliminated from
those equations which are employed to formulate experimental
data.

Assuming then the presence of free electrons as representative
of some condition which may be tentatively evaluated in terms of
electron pressure, electron concentration, or electron activity,
let us consider the electrons to obey the laws of an ideal solution,
their concentration thus being amenable to the law of mass action.

Then, for the equilibrium between ferrous and ferric ions we may
write

[Fe+++] [e]

~pe^r=KFe

Let the symbol [RED] stand for the concentration of a reduc-
tant and [OX] for the concentration of the reductant's oxidation
product. Then, in general, for the type of reaction represented
below where n electrons are concerned we have the equilibrium
equation (48)

OX + ne^ RED

[OX][e]"=K] (48)

[RED]

M-V*^

REDUCTION POTENTIALS 249

For the reaction 2H+ + 2e ^ H2 the equilibrium equation is

[H+]2 r*i2

[H,

= KH (50)

In (50) [H2] refers to the concentration of molecular hydrogen
in solution. Since we shall deal with the partial pressure of
gaseous hydrogen, as is the custom, we introduce [H2] = K P
where K is the equilibrium constant and P is the partial pressure
of gaseous hydrogen expressed in atmospheres. Collecting con-
stants we have

[H+Ne]2

= KH

[e] = ^K,

[H+]2

By the same procedure similar equations can be developed for
any pair of oxidation-reduction products.

We shall now introduce [e] into an equation formulating the
difference of potential between an electrode and an aqueous solu-
tion with which it is in contact.

We shall assume the presence of free electrons in metals, as
is commonly done. We have already postulated free electrons
in solution as the virtual equivalent of the ability of the solution
to give up electrons to a body brought into the solution. We
shall now ascribe to the electrons in the metal phase and to the
electrons in the solution phase activities £m and £s respectively,
defining activity as Lewis has done (see page 278).

The change in free energy accompanying the isothermal trans-
fer of one Faraday of electrons from one phase to the other is

AF = RTln^

If E is the difference of potential between metal and solution and
F the Faraday, EF = A F

Hence : E = — r In £m — In £s

r r

250 THE DETERMINATION OF HYDROGEN IONS

More rigid equations of the same general form have been used
by Herzfeld (1915, 1918), Langmuir (1916), Smits and Aten
(1916), and Reichinstein (1921) and have been derived by reason-
ing on kinetic as well as on thermodynamic theory. Certain
aspects of the following treatment have been developed more
fully by Smits and Aten.

Now in the above equation we have used electron activity.
In order to bring the further treatment into harmony with that
used consistently throughout this book, we shall have to sacrifice
a certain degree of generality and shall imagine that we are
dealing with ver3>- dilute solutions wherein activity approaches
concentration. The like assumption will be made for the activity
of the electrons in the metal. Then we may write

E = — In [e]m - — In [e], . (52)

where [e]m is the concentration of electrons in metal and [e]B the
concentration in the solution.

Substitute for [e]8 its equivalent in any one of the equilibrium
equations and we have a result such as that given below.

For instance, let two hydrogen electrodes be constructed of
the same metal so that when these two electrodes 'are opposed
as in a gas chain the Volta-effect between the electrodes and the
copper of the measuring system will be compensated. The
total E. M. F. of the gas chain is:

VKH
[H+]2
E.M.F. - — In e m - — - In [e]m -+ — In
F F F

VKHii&

If p = P'

„.-„ RT, H+'
E.M.F. = - — In ,- — f-
F IH+]

This is the simplest equation for a hydrogen electrode concentra-
tion cell. In a similar way we obtain the equation for a con-
centration cell of two "reduction potential" electrodes.

It will be noted that in the case mentioned above the terms
containing [e]m certainly cancel out. But will they if for one of

REDUCTION POTENTIALS 251

two like electrodes another of a different metal is substituted?
Whatever the arguments for and against this may be, we believe
that the electrochemical experimental data are quite insufficient to
decide the question. Lest important phenomena be thus obscured,
as Smits believes, the reader should be on his guard; but lest it
be supposed that characteristic differences between different
metals are thus eliminated it may be said at once that these
differences will presently be found to be embodied in a complex
of constants. We shall tentatively assume that the concentra-
tions of the electrons in different metals are sufficiently alike
to permit differences to be ignored for purposes of approximate

treatment and shall regard the term — In [e]m as a constant, Em.

We then have a general equation for the difference of potential

between any electrode and a solution of hypothetical electron

concentration [e]s, namely,

E = Em-^ln[e]s (53)

To obtain an expression relating the potential difference at
an electrode with the equilibria of the ions in solution it is now
only necessary to write a given reaction in a form involving elec-
tron concentration, to solve for [e]8 and to introduce the equiva-
lent of [e]8 in equation (53). Thus the working equation is ob-
tained by a uniform process, and, whatever the limitations
of the development may be, it furnishes at one and the same time
an easy method of remembering electrode relations and a view-
point which helps to clarify the interrelationships of different
systems.

Since it will be convenient to refer all electrode potential differ-
ences to that of the normal hydrogen electrode as the standard,
the nature of the relation will be treated first.

Combine equations (51) and (53) to give

E = Em-^lnyKH

But

TD'T'

——In vKh is a constant which we may call Eh.

252 THE DETERMINATION OF HYDROGEN IONS

Hence

RT \/ P
E = Em-EH-^ln^p (54)

For an oxidation-reduction electrode we have from equations
(49) and (53)

E = Em-^lnK1^PJ
nF [OX]

or, separating the new constant as we have done above, we have

_ „ „ RT, [RED] , N

E = Em_El__lnL__J (55)

If now a normal hydrogen electrode and an oxidation-reduction
electrode be opposed in a "chain" we have from (54) and (55)
the full equation:

E.M.F. = Em - Em + EH - E> + ^ln ^ - ^Inl^S

F LH+] nF [OX]

By definition E in equation (54) is zero when P and [H+] are
unity. Then Em — EH = 0. The above equation then (when
one of the electrodes is the ".normal hydrogen electrode") re-
duces to

E.M.F. = Em-El-f,„^g! («>

It will be noted that the constant in this equation (algebraic
sum of Em and Ei) is not the simple constant of the oxidation-
reduction equilibria, but is a complex. Furthermore the value
is dependent upon the standard of reference used — in this case
the normal hydrogen electrode. The complex nature of this con-
stant has been discussed by Haber.

It is customary to combine such constants as Em and Ei in the
last equation. Furthermore it is convenient to maintain the
same basis of reference, the normal hydrogen electrode. When
this is done it shall be indicated by using for the electrode poten-
tial the symbol Eh.

With these understandings we may at once write equations
for several types of electrode-solution systems.
For the hydrogen electrode

Eh = _?Tln^4: (57)

F [H+l

REDUCTION POTENTIALS 253

For the oxygen electrode

RT, [OH-]
Eh = Ek0-—ln-V-^i (58)

b VP02
For an oxidation-reduction electrode

F v _RT [RED] . .

Eh - Ekl ^f ln ToxT (59)

For a metal electrode in contact with solution containing metal
ions of the electrode metal

RT _[ML

nF n[Mn+]

Eh=E;-— ln^r (60)

Here [M]8 is the hypothetical concentration of metal in solution
supposedly in equilibrium with the electrode. [Mn+] is the con-
centration of metal ions with n positive charges.

If [M], = K[M]m, where [M]m is the concentration of undisso-
ciated metal in the electrode and K is the equilibrium constant,
We may substitute and collect constants thereby obtaining:

Eh„r_RTIn[M]m

nF [Mn+]

If the particular metal is always of the same density and state,
and its electron concentration is constant (compare Smits), we
can regard [M]m in the above equation as constant and so obtain
equation (61) which is customarily used to relate the poten-
tial difference at a given metal electrode to the concentration of
the metal ions in the solution .

Eh = EM + ?£ In [M*+] (61)

The potentials of amalgam electrodes may be derived in a com-
parable way.

In correlating all equilibria about the hypothetical electron
concentrations of solutions, and connecting each in an electrode
potential equation by means of equation (53) there is made evi-
dent a definite interrelationship of all reactions involving elec-
tron transfer. In the elementary development given, rigidity
has been sacrificed for the sake of a simplicity which it is believed
represents relations with sufficient truth to indicate the following
important matters easily overlooked.

254 THE DETERMINATION OF HYDROGEN IONS

In the first place it is readily perceived that it is a mere matter
of choice whether we regard a given electrode to be acting as an
"oxidation-reduction electrode" or as a hydrogen electrode;
and it only requires extension of the same principle to show that
this same electrode can be considered as a metal electrode in
equilibrium with a solution of its own ions. As indicated on
page 245 a platinum electrode immersed in a solution of ferrous
and ferfic ions if treated as a hydrogen electrode, furnishes a
hydrogen pressure which can be considered only as a "calcula-
tion value." By a similar procedure it can be shown that the
estimated platinum-ion concentration would be a mere "calcula-
tion value" so that we naturally avoid considering the electrode
in this case as anything other than a means of picking up elec-
trons in their transfer between Fe++ and FC+++.

Likewise a platinum electrode immersed in a solution may be
said to function as an actual hydrogen electrode only when a
finite concentration or pressure of hydrogen is known or provided.
For such a pressure to be definite and stable the solution must
be reduced to such an extent that any oxidation-reduction equi-
librium in the solution is at a state compatible with the state of
the equilibrium of the reaction:

2H+ + 2e ^ H2

which is under measurement. This is another way of stating
the principle discussed on page 244.

Another interesting relation is obtained by taking into consid-
eration a certain hypothetical relation between the hydrogen
electrode and the oxygen electrode. There are reasons for be-
lieving that an oxy-hydrogen gas cell, i.e., a cell composed of a
hydrogen and an oxygen electrode, each under one atmosphere
of the respective gases should show an E.M.F. of 1.23 volts at
all pH values. It is at once evident then that an oxygen elec-
trode should enable one to measure pH values (see equation (58)),
Or more directly pOH values. As a matter of fact the oxygen
electrode" does not work well in practice and although Grube and
Dulk (1918) believe that they have obtained experimental evi-
dence for the theoretical relation between the oxygen electrode
and the hydrogen electrode, the oxygen electrode is by no means
a practical instrument. Why this is so has been a matter for

REDUCTION POTENTIALS 255

considerable debate. No satisfactory explanation has been of-
fered. If, however, we assume the theoretical relations as a basis
for argument, it is evident from what has already been said that
we are privileged to express the relations between different
electrodes in terms of an oxygen electrode. Likewise it is evident
that to obtain an actual oxygen electrode potential it would be neces-
sary to oxidize the material in solution to a point compatible with
a definite and finite oxygen pressure.

Leaving out all question of the numerical value of the oxy-
hydrogen electrode and all question regarding the actuality of
a hydrogen or oxygen pressure the genesis of equations (57) and
(58) shows that a system can be defined in terms of either a hy-
drogen electrode or an oxygen electrode.

In the second place experimental data obtained with elec-
trode measurements alone do not reveal the components which
enter into the constant of an electrode potential equation. We
shall presently deal with some relations between oxidation-reduc-
tion potentials and the pH of the solution, and shall adopt for the
sake of convenience the assumption that the reductant is an
anion created from the oxidant by the introduction of one or more
electrons. But the equations used to formulate the experimental
data require only that proper relative relations be observed and
it would be just as legitimate to consider the relation between
oxidant and reductant from either of the following points of
view:

OX + 2e ^± RED

OX + H2 ^ hydrogenated reductant.

The same form of electrode equation is obtained in either case
and the decision between the two points of view is inextricably
bound up in the complex nature of the constants which enter
into the working equations.

Thirdly, it is of great practical importance for many studies
to note: that in any case where a definite potential difference is
to be established at the electrode there must be in the system two
species, one of which is the direct or indirect reduction product of
the other, and that the ratio of their concentrations or activities
must be of finite magnitude. Neglect of this principle is not

256 THE DETERMINATION OF HYDROGEN IONS

infrequent, and is doubtless due to the emphasis which has been
placed upon the final, working form of the equation for the dif-
ference of potential betwreen a metal and a solution of its ions. In
obtaining the final form of this equation certain assumptions
have been made and the potential difference at the electrode is
made to appear as if it were dependent only upon the concentra-
tion of one species, namely the metal ions. Whether this be
the explanation or not, there are not infrequently encountered
in the literature attempts to measure electrode potential differ-
ences with a single oxidant or reductant. It should be plain
from a study of figure 39 that, when the oxidant or reductant
alone is present, the electrode potential difference becomes asymp-
totic to the Eh axis. Were it possible to eliminate absolutely
every trace of the oxidant, the potential difference obtained with
the reductant alone would tend to become infinite. Wherever
stable potentials have been reported as having been found with
reductant alone it is doubtless due to the presence of the oxidant
as an impurity.

From the foregoing discussions it should be evident that the
designation of a particular electrode-solution system depends so
far as convenience is concerned upon relations which we seek,
it being more convenient in some instances to formulate all data
in terms of hydrogen electrode potentials and in other instances
in terms of reduction potentials. So far as the actual physical
maintenance of electrode conditions is concerned the designation
of an electrode as of one or the other type will certainly depend
upon a finite ratio of two products, one of which is the reduction
product of the other; but the discovery of what these species
are is often a most difficult problem for the solution of which the
electrode equations by themselves are not sufficient.

SOME ELEMENTARY RELATIONS OF HYDROGEN ION CONCENTRA-
TIONS TO OBSERVED " REDUCTION" POTENTIALS

In dealing with an oxidation-reduction equilibrium, as, for
instance, that between ferrous and ferric iron, our first concern
is with the relation between electrode potential difference and
the ratio of the concentrations of the components added, or
analytically determined. Now it is found that a given ratio of
ferric arid ferrous salts does not give the same potential under

REDUCTION POTENTIALS 257

all circumstances as it should if we could substitute this fixed
ratio in Peters' equation. It is convenient to assume that the
true ratio to be substituted is the ratio of the ion concentrations
and when this ratio can be found its substitution in Peters' equa-
tion often yields a good constant. Alteration of the ion concen-
tration from that of the total salt added may be due to incomplete
ionization of the salt as added or to the withdrawal of ions by
the formation of complexes. Very often the concentration of
the active agents is determined by the concentration of the hydro-
gen ions and it is with this that we are now concerned.

To illustrate the problem let us assume that the active oxidant
is neither acidic nor basic so that we can neglect any acidic or
basic dissociation and in dilute solution identify the active con-
centration [OX] with the total oxidant [S0]. Let us next assume
that on reduction an electron is introduced into the body to
make the reductant virtually acidic. The concentration of
active reductant then becomes the concentration of the anion
of an acid. [RED] must be identified as [RED], and, when there
is sought the relation between observed potentials and total
reductant and oxidant, use must be made of the equation for

the acid dissociation : [RED] = — — I" r * where [SJ is the total

concentration of reductant and Kais the acid dissociation con-
stant for that particular seat of ionization concerned. Substitut-
ing the above in equation (59)

Eh = Ekl-^lnKa+^
nF nF

lnT^-MH^l-— In^}
L J nF [S0]

or collecting constants

Eh=Ek+Hln[K. + [H+]]-?flng (62)

In order to emphasize the effect of [H+] let us assume that the

. [SJ .
ratio — , is to be kept constant while [H+] is varied. Inspec-
ts

tion of (62) shows that while [H+] is large in relation to Ka, Eh

will vary as -^ In [H+]. When [H+] approaches and passes

Ka, variation of Eh passes over gradually from the relation indi-
cated above to the other extreme where there is no appreciable
variation of potential with change in [H+],

258 THE DETERMINATION OF HYDROGEN IONS

Ordinarily these relations are not perceived because the varia-
tion of [H+] is insufficient, but the principle involved is to be
found in the case of ferro-ferricyanide potentials as pointed out
by Kolthoff, and they are more clearly to be perceived in the
data on the oxidation-reduction potentials of certain dyes briefly
reported by Clark (1920) and by Clark and coworkers (1921).

Let us also consider the equilibria of the quinone-hydroqumone
system.

Quinone + 2d -ctrons ;=± anion of hydroquinone
OCtH40 + 2e^ OC6H40

If in equation (59) we identify [OX] as the total concentration
of quinone, [Sq], then in the same equation [RED] must be iden-
tified as the concentration of the divalent anion of hydroquinone
[TT], and n = 2.

*-*--wMw (63)

If [Sd] is the total concentration of hydroquinone, [H2D] the
undissociated hydroquinone, [HD] the first anion, [D] the second
anion, Ki the first acid dissociation constant and K2 the second
acid dissociation constant we have:

[hd] [h+] _ mm _ ~

~vm~ ~ "IhdT ~ '

and

[Sd] = [H2D] + [HD] + [ D~]

Solving the above equations for [ D ] and substituting in (63) we
have:

Eh-Efc-H lnKaK.+^ln

[H+l'+KitH+J + KxK,

]

-— In ^3 (64)

2F [SJ K }

The second term can be combined with Ekl to give E'k as will
be done later.

We shall consider only the order of magnitude of Ki and K2
and their combined influence. Scudder's tables give Ki =
1 X 10"10. Let K2 be assumed to be of the order 10-11. Neg-

REDUCTION POTENTIALS 259

lecting numbers of insignificant orders of magnitude we find that
while [H+] is large in relation to Ki and K2 (higher than 10~7)

the third term in equation (64) reduces to + "^ In [H+]2.

Then

0.000,198T [Sa] , x

Eh = Ek - 0.000, 198TpH - £ log — j (65)

Thus, if the ratio of total hydroquinone to total quinone be
kept constant, the electrode potential difference, Eh, is a linear
function of pH within the limits of the assumptions made above.
A departure from this relation should begin to appear near pH
9, should become very marked at pH 10, and, if other phenomena
could be ruled out, Eh should no longer vary with pH when pH
is larger than about 12 provided the magnitude of K2 has been
correctly guessed.

The experimental data to be mentioned in a later chapter indi-
cate that the hydrogen pressure in equilibrium with an equimolec-
ular mixture of quinone and hydroquinone is physically of an
entirely negligible magnitude.

As Biilmann has shown (see Chapter XX), a platinum electrode
in the presence of a definite mixture of quinone and hydroquinone
can be made to measure pH values.

Besides cases of the type given above we have cases such as
that of iron where the reaction

Fe+++ + e ^± Fe++

is essentially the destruction by the electron of a point of basic
ionization.

It is also conceivable that the addition of two electrons may
change an ampholyte to a diacidic compound.

Available data are quite insufficient to show whether or not
ionizations at points other than those immediately concerned
in the oxidation-reduction process produce a marked effect upon
the point actually concerned in the oxidation-reduction process.
They probably do for any strain in the electronic forces at one point
of a molecule must be felt to some extent at all other points.

There may also be found cases where the electronic fields of
force are so altered by the introduction of the electrons concerned

260 THE DETERMINATION OF HYDROGEN IONS

in reduction that the reductant, instead of becoming more acidic
or less basic becomes less acidic or more basic. The system hemo-
globin-oxyhemoglobin comes to mind; but the available data are
altogether too meagre to permit a formulation of actual cases,
or even to permit an appraisal of the present method of presenta-
tion. We have only to keep in mind the fact that, if this method
of treatment proves to be valuable, there may be found a wide
variety of cases reducible to a form comparable with that of
equation (62). There we find three terms. Of these the middle
term is the one which will vary from case to case. It will con-
tain [H+] and the constants of the oxidation-reduction equilib-
rium. This term will determine, not only the general form of the
curve relating Eh to [H+], but also deviation or inflexion points

fS 1
when 7£~. and n are kept constant and [H+] is varied.

Whenever the magnitudes of the equilibrium constants are in

such relation to [H+] that the middle term reduces to -^ In

[H+], as it may in (64), the electrode potential becomes a linear
function of pH. Under these limited circumstances there can
be calculated a hypothetical, constant, hydrogen pressure by the
method given at the beginning of this chapter, — which pressure
may be considered characteristic for the given equilibrium. Since
such pressures are often of very small magnitude, and since they
vary in magnitude even more than hydrogen ion concentrations,
it is sometimes convenient to use a logarithmic system of no-
tation similar to the pH of hydrogen electrode work and to let

log — — = rH, where Ph2 is the pressure of molecular hydrogen

in atmospheres.

Clark and coworkers have calculated rH values characteristic
of various oxidation-reduction indicators. Examples are shown
in table 45.

As indicated above such rH values have a limited significance.
Even near neutrality the indigo system departs from constant
rH and in a manner indicated by a full equation comparable with
(64).

The manner in which the three variables — electrode potential,
pH and percentage reduction, are related in certain cases is
illustrated in figure 39.

REDUCTION POTENTIALS

261

When it is desired to express the state of a solution without
regard to any particular equilibrium it is best to return to the
concept formulated in equation (53) as having the desired gener-
ality. But lest terms such as electron concentration, pressure
or activity gain an unwarranted appearance of reality through use,
and lest numerical values connected with this concept be given
meanings too arbitrary, it will be best to retain the use of the elec-
trode potentials themselves and in general to call them reduction
potentials. These specify with directness the general state of the
solution.

TABLE 45

INDOPHENOL-INDOPHENOL WHITE

TETRA SULFONATES OF INDIGO AND
OF INDIGO WHITE

4.36

21.3

3.09

12.2

5.33

21.4

4.51

12.2

6.64

22.0

5.90 •

12.3

7. DO

21.4
20.7

6.48

12.5

8.98

10.23

20.5

As pH increas

;s rH increases

Since a given mixture of oxidation and reduction products
at a given pH stablizes the "reduction potential" of a solution,
we have a condition comparable with the buffer action in the
acid-base system. To distinguish stabilization of oxidation-
reduction from acid-base buffer action we may use the term
poising action. Thus a solution may be said to be poised at
a given reduction potential when the addition or subtraction
of oxidants or reductants does not seriously alter the reduction
potential.

For example in figure 39, if methylene blue at pH 4.6 is about
75 per cent reduced we know that the reduction potential of the
solution should be at about +0.1. If quite appreciable additions
of oxidants or reductants do not displace the reduction potential
very much from this point it is evident that the solution is " poised"
at + 0.1.

This brief outline will have indicated the profound importance
of the hydrogen ion concentration of a solution for processes of

262

THE DETERMINATION OF HYDROGEN IONS

oxidation-reduction. A striking demonstration is given in a
lecture experiment by Stieglitz (1917, page 292). Formaldehyde
in acid solution is comparatively inactive with silver ions. On
alkalization of the mixture vigorous reduction of the silver occurs.
It may also be shown that a proper mixture of ferro- and ferri-
cyanid is inactive toward indophenol in neutral and alkaline
solutions, that up to acidities of pH 4 the potential of the ferro-
ferri mixture does not vary with pH while that of indophenol-
indophenol white does. At acidities near pH 4 the two systems
run into one another and the indophenol is reduced.

100

I>vA.tc^O

'fl

•Wry/

•ail

\ \
J

+.3

100'

S<?

;' ;'

' i

°m. B\vt

'J\

+,* +.3 +.2. +•' ° -I -\

Fig. 39. Relation of pH to Oxidation-Reduction Equilibria of Indigo-
Indigo White and Methylene Blue-Methylene White

Abscissas: reduction potential. Ordinates: percentage reduction. Fig-
ures on curves: pH values.

Finally it may be said that all oxidation-reduction equilibria
do not lend themselves equally well to potent iometric study. An
enormous amount of experimental and theoretical investigation
remains to be done.

In passing, it may be mentioned that the instruments and many
of the principles which have been here described for the determina-
tion of hydrogen ion concentration are applicable in the deter-

REDUCTION POTENTIALS 263

mination of oxidation-reduction equilibria and in the titration of
oxidizing or reducing substances. The oxidation-reduction elec-
trode with potentiometric measurement has been applied exten-
sively to the determination of the end points of titrations and to
the -study of oxidation-reduction equilibria.

While the effect of hydrogen ion concentration has been recog-
nized in many of these studies altogether too little use has been
made of the methods which have been applied in biochemistry
for the control and measurement of pH.

CHAPTER XVII
Sources of Error in Electrometric^ Measurements of pH

Besides faults in the potentiometric system there are a variety
of sources of error which demand special attention. Some of
these are specific to hydrogen electrode work; others are not.

Sometimes the most trivial occurrence may cause considerable
trouble; such is the bubble of gas that may persistently cling to
the bore of a stopcock key which is part of a liquid connection.
This is mentioned simply to emphasize the constant watchfulness
required of the operator of a hydrogen electrode system. A well-
shielded electrical system may be put out of commission in the
most unexpected way. Miserly supply of hydrogen with which
to sweep out hydrogen electrode vessels is perhaps one of the com-
monest faults, but the hoarding of solutions which should be used
to rinse away the buffer action of solutions previously used in a
vessel may also be serious.

Aside from such questions of technique there are certain inher-
ent difficulties in the application of the hydrogen electrode method.

We have already discussed in Chapter XVI the relation between
the hydrogen electrode and the "reduction electrode," and have
shown that no true hydrogen electrode potential can be attained
until the solution is so far reduced that it can support one atmos-
phere of hydrogen. It is thus made perfectly obvious that a meas-
urement of pH must be preceded by a very thorough reduction
of the solution.1

When we speak of reduction we mean reduction in its wide sense
and include among the oxidizing agents those metal ions which
at a given concentration may be reduced by one atmosphere of
hydrogen.

The hydrogen electrode if properly treated gives such a pre-
cisely defined potential in certain well buffered inorganic solutions,
reaches this potential so rapidly, returns when polarized, and

1 In some instances it is important to remember that reduction of the
constituents of a solution may so change the acidic or basic properties of
these constituents that serious shifts in pH may occur.

264

ERRORS IN ELECTROMETRIC MEASUREMENTS 265

adjusts itself to temperature and pressure changes so well that there
is little doubt of its being a reversible, accommodating, relatively
quick-acting electrode. It is perhaps because of this that it shows
a hydrogen electrode potential in solutions which could be slowly
reduced by hydrogen. For instance certain culture media may
exhibit upon an electrode of platinum uncharged with hydrogen •
a potential which is distinctly toward the oxidizing region of oxi-
dation-reduction potential. That they are capable of reduction
and that the first reduction potential is not a pseudo potential
is shown by the orderly progress of the potential toward that of a
hydrogen electrode under the activity of bacteria. Yet such
culture media if treated in the first place as in making a hydro-
gen electrode measurement exhibit a fairly constant and repro-
ducible hydrogen electrode potential the calculated pH value
from which checks well with colorimetric measurements. The
explanation seems to be that although that complete reduction
of material to a point where the oxidation-reduction equilibrium
will support an atmosphere of hydrogen is not attained, there is
established a virtual hydrogen electrode equilibrium by reason
of the rapidity of action between hydrogen and hydrogen ion and
the slowness of action between hydrogen and oxidizing agents.

The effect of an intense oxidizing agent will be at once recognized.
At the other extreme are the cases where no drift in the E. M. F.
in the direction of an oxidizing action at the hydrogen electrode
will be detected. Between these extremes lie the subtle uncer-
tainties which make it advisable to check electrometric measure-
ments with indicator measurements and to apply tests of repro-
ducibility, of the effect of polarization, of the effect of time on
drift of potential and all other means available to establish the
reliability of an electrometric measurement in every doubtful case.

There are effects of unknown cause which are included under
the term "poisoned electrodes." An electrode may be "poisoned"
by a well defined cause such as those to be mentioned presently;
but occasionally an electrode will begin to fail for reasons which
cannot be traced. There is hardly any way of putting an ob-
server on his guard against this except to call his attention to the
fact that if he is familiar with his galvanometer he will notice a
peculiar drift when balancing E. M. F.'s.

Arsenic deposits, adsorption of material by the platinum black

266 THE DETERMINATION OF HYDROGEN IONS

(with such avidity sometimes that redeposition of the black is
necessary), the deposit of films of protein, have all been detected
as definite causes of electrode "poisoning." Michaelis (1914)
places free ammonia and hydrogen sulfid among the poisons.
However, there is no special difficulty in obtaining hydrogen
electrode potentials agreeing with colorimetric measurements in
bacterial cultures containing distinct traces of ammonia or hydro-
gen sulfid and apparently reliable measurements have been made
of the pH values of ammonium-ammonium chloride mixtures.
' Of the antiseptics used in biological solutions Michaelis (1914)
states that neither chloroform nor toluol interfere if dissolved.
He does not mention that chloroform may hydrolyze to hydro-
chloric acid. Drops of toluol however affect the electrode.
Phenol is permissible but of course in alkaline solutions partici-
pates in the acid-base equilibria.

There is an extensive literature upon the so-called "poisons"
which interfere with the catalytic activity of the finely divided
noble metals used on the hydrogen electrode. This literature is
most suggestive, but there is still need for more direct studies of
the conditions surrounding the catalytic activity of the hydrogen
electrode.

Simply for the sake of clearness we may distinguish two func-
tions of the electrode. The electrode is first of all a convenient
third body by which there is established electrical connection
with the system hydrogen-hydrogen ions. That the equilibrium
of this system should not be disturbed by the presence of a sub-
stance "poisoning" the catalytic activity of the platinum black
has been tacitly assumed in the derivation of the thermodynamic
equation for electrode potential difference. If the reduction of
the solution could be accomplished without dependence upon the
catalytic activity of the electrode it should be theoretically possi-
ble to attain a true hydrogen electrode potential even in the pres-
ence of a "poison." However, in ordinary practice an electrode
is used not only as an electrode per se but also as a hydrogenation
catalyst. As such it is very sensitive to "poisons." "Poisons"
are then to be regarded as the cause of sluggish electrodes. Among
these we find all degrees. Hydrogenation to a point compatible
with a true hydrogen electrode potential may be delayed but
slightly and we may say that the electrode is a bit slow in attain-
ing a stable potential without our ever suspecting a "poison;"

« ERRORS IN ELECTROMETRIC MEASUREMENTS 267

or the black metal may be so seriously injured that it becomes
entirely impractical to await equilibrium.

And just as " poisons" may render an electrode useless for practi-
cal measurements, so the employment of accelerators of catalysis
may promote efficiency. With the exception of a brief, unpublished
note by Bovie little work has been done in this direction.

From what has already been said the effect of the presence of
oxygen is obvious. Indifferent gases such as nitrogen may be
considered merely as diluents of the hydrogen and as such must
be taken into consideration in accurate estimations of the partial
pressure of hydrogen. Gases like carbon dioxid on the other
hand act not only as diluents but also become components of
any acid-base equilibrium established in their presence.

In very many instances biological fluids contain carbonate and
the double effect of the carbon dioxid upon the partial pressure
of the hydrogen and upon the hydrogen ion equilibria render accu-
rate measurements difficult unless both effects are taken into con-
sideration and put under control.

At high acidities in the neighborhood of pH 5 carbon dioxide
will have relatively little effect upon a solution buffered by other
than carbonates. As the pH of solutions increases the participa-
tion of C02 in the acid-base equilibria becomes of more and more
importance. The C02 partial pressure in equilibrium with the
carbonates of a solution is a function of both the pH and the
total carbonate. If, however, we consider for the sake of the
argument that the total carbonate remains fairly low and constant,
the C02 partial pressure becomes less with increase in pH while
its effect upon the hydrogen ion equilibria increases with increase
in pH. Therefore it may be said that it is of more importance
under ordinary conditions to maintain the original C02 content
of the solution than it is to be concerned about the effect of C02
upon the partial pressure of the hydrogen. Furthermore the
effect of diminishing the partial pressure of the hydrogen is of
relatively small importance.

For these reasons the bubbling of hydrogen through the solu-
tion is to be avoided unless one cares to determine the partial
pressure of C02 which must be introduced into the hydrogen to
maintain the carbonate equilibria and then provides the proper
mixture (Hober). The method usually employed is to use a vessel
such as that of Hasselbalch, of McClendon or of Clark in which a

268 THE DETERMINATION OF HYDROGEN IONS ♦

preliminary sample of the solution can be shaken to provide the
solution's own partial pressure of C02, and in which there is provi-
sion for the introduction of a fresh sample with its full C02 pressure.
The hydrogen supply is then kept at atmospheric pressure and
the partial pressure of hydrogen in the electrode vessel is either
considered to be unaffected by the C02 pressure or corrected from
the known C02 pressure of the solution under examination.

Of course in cases where the total carbonate in solution rises to
considerable concentrations the partial C02 pressure may become
of very significant magnitude and its effect in lowering the hydro-
gen pressure must be carefully considered.

In determining the hydrogen ion concentration of the blood by
the electrometric method the two outstanding difficulties encoun-
tered are the presence of carbonate and oxyhemoglobin. If hy-
drogen is swept through the fluid it will remove so much of the
C02 that the hydrogen ion concentration is lowered. If hydrogen
is not swept through, the C02 will escape into the hydrogen at-
mosphere about the electrode and reduce the partial pressure of
the hydrogen. The oxygen present in the oxyhemoglobin "de-
polarizes" the hydrogen' electrode and makes necessary the
employment of the plasma.

Evans (1921) has maintained that in the electrometric measure-
ment of carbonate solutions the carbonate is reduced to formate
and that for this reason previous measurements of the pH of
blood have been in error. There are various theoretical reasons
for doubting the validity of Evans' last conclusion; but since the
question is one of fact Cullen and Hastings (1922) have investi-
gated the matter and have failed to confirm Evans.

The criterions of a good hydrogen electrode measurement are
difficult to place upon a rigid basis but certain practical tests
are easy to apply. Reproducibility of an E. M. F. with different
electrodes and different vessels is the foremost test of reliability,
but not a final test. Second is the stability of this E. M. F. when
attained. It is not always practicable to distinguish between a
drift due to alteration in the difference of potential at liquid
junctions and a drift at the electrode but in most cases the drift
at the liquid junction is less rapid and less extensive than a drift
at the electrode when the latter is due to a failure to establish a
true hydrogen-hydrogen ion equilibrium. A test which is some-
times applied is to polarize the hydrogen electrode slightly and

ERRORS IN ELECTROMETRIC MEASUREMENTS 269

then see if the original E. M. F. is reestablished. This may. be
done sufficiently well by displacing the E. M. F. balance in the
potentiometer system. Where salt and protein errors do not in-
terfere the gross reliability of a hydrogen electrode measurement
may be tested colorimetrically. This checking of one system with
the other is of inestimable value in some instances as it has proved
to be in the study of soil extracts. There the possibilities of vari-
ous factors interfering with any accurate measurement of hydrogen
ion concentration dimmed the courage of investigators until Gil-
lespie (1916) demonstrated substantial agreement between the
two methods. Subsequent correlation of various phenomena
with soil acidity so determined has now established the useful-
ness of the methods.

In addition to the tests so far mentioned there remains the test
of orderly series. Certain of the general relations of electrolytes
are so well established that, if a solution be titrated with acid or
alkali and the resulting pH values measured, it will be known from
the position and the shape of the "titration curve" whether the
pH measurements are reasonable or not. This of course is a
poor satisfaction if there is any reason to doubt the measurements
in the first place but it is a procedure not be scorned.

In dealing with protein solutions Robertson (1910) found that
the electrode was injured by deposits of protein which he as-
cribed to acid coagulation of the protein by the acid absorbed
in the platinum black from previous measurements. Robertson
therefore recommends that in a series of measurements with
protein solutions the series be treated from the alkaline to the
acid solutions. If his explanation be true there are instances
where the reverse procedure should be followed. See sections
on isoelectric points.

Not infrequently the attempt is made to measure electrometri-
cally the pH value of an unbuffered solution such as that of KC1.
It is not entirely the fault of the method but rather of the nature
of the solution that this is a task requiring the very highest
refinements known to experimental art. If for the sake of the
argument we assume that the solution under examination is that
of a perfectly neutral salt having under ideal conditions a hydro-
gen ion concentration of 0.000,000,1 N, a simple calculation will
show what an enormous displacement in pH will be caused by
the admittance of the slightest trace of CO2 from the atmosphere,

270 THE DETERMINATION OF HYDROGEN IONS

of alkali from a glass container, of impurities occluded in the
electrode or of impurities carried into the solution with the sol-
vent or solute. Conversely, even if the measurement were such
as to give the true value under ideal conditions it would have
little practical significance because of the difficulty in holding the
conditions ideal.

By the same reasoning it appears probable that it would be
difficult to obtain true electrode potentials even with a potentio-
metric system drawing no current during its adjustment. When
no buffer is present there is a negligible reserve of hydrogen ions.
But the introduction of the electrode with its enormous surface
must displace the equilibrium. How much the displacement
will be depends both on relative proportions of electrode and
solution and on the technique used.

The effect of temperature variations upon the accuracy of
electrometric measurements is a question upon which it is difficult
to pass judgment. Of course, if measurements are not intended
to be refined one may assume the temperature of the room to be
the temperature of the system at the moment of the electrical
measurement. It is then a simple matter to select from tables
the values and factors applicable at the selected temperature.
Since such a procedure introduces errors which are not serious
for many purposes the author's insistence upon temperature regu-
lation has been criticized. Those who take this position are doubt-
less able to escape the psychological effects of uncertainty, but
they can hardly escape the inconvenience of having to deal with
new values and new factors with every shift in temperature.
Temperature control so simplifies rough measurements that much
.time is saved, and for this reason is recommended even when it
is unnecessary. But before the practice of neglecting tempera-
ture control can have scientific standing it needs more experi-
mental investigation than it has been accorded. Calculations
are quite insufficient -for we have little data upon the hysteresis
in the adaptation of different systems to temperature variation.

Cullen (1922), finding that the temperature in an electrode
vessel is seldom that of the surrounding air in a room subject to
temperature variation, has devised a modification of the Clark
electrode vessel whereby the temperature of the solution can be
measured. The same modification can easily be made in a calo-
mel electrode vessel.

• CHAPTER XVIII

Standard Solutions for Checking Hydrogen Electrode

Measurements

Id. the routine measurement of hydrogen ion concentrations it
is desirable to frequently check the system. To do so in detail
is a matter of considerable trouble ; but if a measurement be taken
upon some solution of well defined pH, and it is found that the
potential of the chain agrees with that determined by careful and
detailed measurements upon all parts, it is reasonably certain
that the several sources of E. M. F. are correct.

Any one of the buffer mixtures whose pH value has been estab-
lished may be used for this purpose, but there are sometimes
good reasons for making a particular choice.

S0rensen (1909) used a mixture of 8 volumes of standard gly-
cocoll solution to 2 volumes of standard hydrochloric acid solution
for the details in the preparation of which see page 109. Michaelis
(1914) recommends what has come to be known as "standard ace-
tate." This is a solution tenth molecular with respect to both
sodium acetate and acetic acid. Its preparation and hydrogen
electrode potential at 18°C. have been carefully studied by Wal-
pole (1914). Walpole proposes two methods for its preparation:

(1) From N-sodium hydroxid solution free from carbon dioxid and
N-acetic acid adjusted by suitable titration (using phenolphthalein), so as
to be exactly equivalent to it.

(2) From N-sodium acetate and N-acetic acid adjusted by titration of
a baryta solution, the strength of which is known exactly in terms of the
N-hydrochloric acid solution used to standardize electrometrically the
normal solution of sodium acetate .

Walpole defines N-sodium acetate as a "solution of pure sodium
acetate of such concentration that when 20 cc. are taken, mixed
with 20 cc. of N-hydrochloric acid, and diluted to 100 cc. the
potential of a hydrogen electrode in equilibrium with it is the same
as that of a hydrogen electrode in equilibrium with a solution 0.2
normal with respect to both acetic acid and sodium chloride."
By mixing the N-acetate with the N-HC1 in accordance with this

271

272

THE DETERMINATION OF HYDROGEN IONS

definition and then determining the potential of a hydrogen elec-
trode in equilibrium with it Walpole shows that the N-sodium
acetate solution may be accurately standardized. In the fol-
lowing table are given Walpole's values showing the relation of

TABLE 46

CUBIC CENTIMETERS OF N/1 HC1 TO 20 CUBIC

CENTIMETERS N/1 NaAc DILUTED

TO 100 CUBIC CENTIMETERS

E. M. F.

19.00

0.5270

19.40

0.5155

19.50

0.5125

19.90

0.4945

20.00

0.4898

20.39

0.4712

20.89

0 4549

21.00

0.4525

the E. M. F. of the chain: Hg | Hg2Cl2 KC1 (0.1m) | KC1 (sat.) | Ace-
tate | H2Pt at 18°, to the cubic centimeters of N-HCladdedto20cc.
N-sodium acetate and diluted to 100 cc. If, for instance, the

potential found is 0.4800 volts, the ratio

Concentration of Na Ac

Hence the sodium acetate is 0.9901N.

20.2
20.0'

These values are more convenient to use if plotted as Walpole
has done.

TABLE 47

TEMPERATURE

E. M. F.

TEMPERATURE

E. M. F.

0.5170

0.5180

0.5171

0.5183

0.5172

0.5186

0.5174

0.5190

0.5175

0.5195

0.5178

34-38

0.5200-0.5205

Walpole found that the E. M. F. of the chain: Pt H2 1 "standard
acetate" |sat. KC1| 0.1m KC1 Hg2Cl2| Hg at 18°C. is 0.6046. The
contact potential still to be eliminated was estimated by the
Bjerrum extrapolation to be 0.0001 volt. Hence the true poten-

STANDARDS FOR CHECKING

273

tial is 0.6045. This value seems to be the value of the chain
corrected to one atmosphere hydrogen plus vapor pressure.

Michaelis (1914) gives the values in table 47 for the difference of
potential between the saturated KC1 calomel electrode and the
hydrogen electrode in his standard acetate.

It will be noted that both S0rensen's standard glycocoll and the
standard acetate solutions must be constructed by adjustment of
the components. While there is no great difficulty in this there
remain the labor and the chance of error that are involved. Clark

KHFhtkiUtc

C.C.

Fig. 40. Titration of Phthalic Acid with KOH

and Lubs (1916) have shown that acid potassium phthalate pos-
sesses, a unique combination of qualities desirable for the standard
under discussion. The first and second dissociation constants of
phthalic acid are so close to one another that the second hydro-
gen comes into play before the first is completely neutralized (see
fig. 40). As a consequence the half-neutralized phthalic acid
(KHPhthalate) exhibits a good buffer action. The salt of this
composition crystallizes beautifully without water of crystalliza-

274

THE DETERMINATION OF HYDROGEN IONS

tion, and, as was shown .by Dodge (1915) and confirmed by
Hendrixson (1915) it is an excellent substance for the standard-
ization of alkali solutions. As such it is used to standardize the
alkali entering into the buffer mixtures of Clark and Lubs (see
page 102) . The outstanding feature is that the ratio of acid to
base is fixed by the composition of the crystals and not by ad-
justment as in other standards. The salt may be dried at 105°C.
and accurate concentrations constructed. The diffusion potential
against saturated KC1 is somewhat higher than that of standard
acetate as estimated by the Bjerrum extrapolation but not so
high as to make good readings difficult.
Clark and Lubs (1916) found for the chain:

. HgHg2Cl2 | KC1 (saturated) | M/20 KHPhthalate | H2 Pt

at 20°C. an E. M. F. of 0.4807 corrected to one atmosphere of
. hydrogen. Their saturated calomel electrode was 0.0882 volt
more negative than the average of a set of tenth normal calomel
I electrodes. Assuming 0.3379 (cf. Chapter XIX) as the value of
• the tenth normal calomel electrode and 0.0004 volt for the dif-
fusion potential still to be eliminated, the hydrogen electrode
potential of M/20 KHPhthalate at 20° is 0.2306.

LJnfortunately the temperature relations of such chains are not
accurately known. For ordinary work the pH of M/20 KHPhtha-
late may be considered as 3.97 between 20° and 30°C. Assuming
a liquid junction potential difference of 0.0004 volts we can reckon
from these data the following total electromotive forces at various
temperatures of the chain :

Calomel electrode of KC1 cone. X

Sat. KC1

Hydrogen electrode
at one atmosphere
in KHPhthalate

(i)

STANDARDS FOR CHECKING

275

TABLE 48

TOTAL E. M. F.

X = 0.lM

X=1.0m

X=saturated KC1
(approximate)

18
20
22
24
26
28
30

0.5675
0.5689
0.5704
0.5719
0.5733
0.5748
0.5763

0.5158
0.5170
0.5181
0.5192
0.5204
0.5215
0.5227

0.4800
0.4802
0.4806
. 0.4812
0.4817
0.4822
0.4827

These values are entirely provisional ftfr temperatures other
than 20°C. and require experimental verification before they can
be used for precise standards. They are given as convenient
standards for ordinary check measurements.

CHAPTER XIX
Standardization of pH Measurements

In the development of the theory of electrolytic dissociation
the hydrogen electrode came upon the scene comparatively late
and after many of the quantitative relations had been established
by conductance data. It was therefore natural that these data
should have been accepted in the standardization of potentio-
metric measurements. It now appears that the interpretation of
conductance data is more complicated than at first supposed and
that certain of the values that have been used in the standardiza-
tion of potentiometric measurements are in doubt. The resulting
confusion demands careful consideration.

Let us review briefly the way in which conductance data enter
into the potentiometric system.

The following equation relates the potential difference, E, at
a hydrogen electrode to the partial pressure, P, of hydrogen, the
concentration of hydrogen ions, C, and the constant K,

RT VP
F c

As shown in a previous chapter we are forced to one or an-
other set of comparisons such as is found in a concentration cell
where P and K are constant. In this case we have a measurable
electromotive force and the relation

RT d
E. M. F. = ^rlnTT

Thus we determine the ratio of two hydrogen ion concentra-
tions if the solutions are sufficiently dilute to permit the applica-
tion of the gas laws from which the above equation was derived.
To apply this equation directly to the determination of either
concentration Ci or C2 the other concentration must be known.
Conductance data have been relied upon to furnish the known
concentration.

Likewise, when a chain composed of a calomel electrode and a

276

STANDARDIZATION OF pH MEASUREMENTS 277

hydrogen electrode is used, the value assigned to the calomel elec-
trode is such that when it is subtracted from the total E. M. F.
of tr?e chain the resulting E. M. F. is as if between a normal hy-
drogen electrode and the hydrogen electrode under measurement.
This implies the experimental determination of the difference of
potential between a normal hydrogen electrode and the calomel
electrode or else between the calomel electrode and a hydrogen
electrode in some solution of known hydrogen ion concentration.
To determine this known hydrogen i«n concentration conductance,
data upon hydrochloric acid solutions have been relied upon.

Unfortunately hydrochloric acid solutions exhibit the so-called
anomalies of strong electrolytes which have already been mentioned.
Although it was known from the first that hydrochloric acid solu-
tions do not obey the dilution law , it was supposed that the ratio
of the equivalent conductances at dilution v and at infinite dilution
(where there is complete dissociation) would give the percentage
ionization at dilution v and hence the hydrogen ion concentration
at this dilution. However, this conclusion involves the assump-
tion that the mobilities of the ions remain unaltered between
dilution v and infinite dilution. Jahn (1900) and Lewis (1912)
have questioned this assumption and within recent years the con-
clusion has become firmly established among many investigators
that the mobilities do change or else that the chemical activity of
the ions of strong electrolytes is not strictly proportional to their
concentration. In other words conductance data alone are not
sufficient to define with precision the hydrogen ion concentrations
of the hydrochloric acid solutions which have been used to stand-
ardize the hydrogen electrode system of concentration chains.
In support of this contention there have been brought forward
comparisons of the concentration chains themselves. There is

evidence that the ratio — in the concentration chain formula

is not necessarily determined with accuracy when a measurement
of the E. M. F. of such a chain is taken. What is it then that is
determined? The' way in which this question will be answered
will doubtless form another interesting chapter in the philosophy
of science. Focused upon this point are two tendencies; the one
seeking to find the factors which interfere with the application of
the simple gas laws so that the experimental data may be corrected

278 THE DETERMINATION OF HYDROGEN IONS

to apply to the "ideal;" the other seeking to formulate either the
empirical data or the thermodynamic relations without special
reference to the mechanisms involved. •

It was an astute suggestion of Lewis (1907) that the simple
thermodynamic relations be assumed to hold, not for concentra-
tion pressure relations, but for quantities which, when introduced
into the equations embodjdng the gas laws, will make these laws
apply. The two new quantities are activity and fugacity. In the
special case of a "perfect" solution, a very dilute solution, obeying
the laws of gases, activity and fugacity are equal to concentration
and pressure respectively. But when a solute ceases to conduct
itself in accord with the laws of gases, its fugacity and activity
remain such that the equations which apply to "perfect" solutions
still hold.

Stated in the above manner it may appear to those who insist
upon looking for the means of applying concentration relations as
if Lewis had made use of a clever dodge. In reality he has simply
expressed in a form which he has developed into a self-consistent
system that which is the more directly determined experimentally.
This is at once evident in the definition of activity by the fol-
lowing postulates.

1. When the activity of a substance is the same in two phases, that
substance will not of itself pass from one phase to the other. 2. When
the activity of a substance is greater in one phase than in another, the sub-
stance will pass from the one phase into the other, when they are brought
together.

With these postulates Lewis proceeds to develop a self-consist-
ent system in which it appears that in a "concentration cell" the
ratio of activities is related to the E. M. F. by the equation

_ ,, _ RT , activity 1

E. M. F. = — In ^—

nF activity 2

Only at infinite, or very high dilution, when a solution approaches
an "ideal" solution, does the more familiar relation of concentra-
tion hold true. So long as the limitations were well understood it
was permissible to speak of the hydrogen electrode method -as a
means of determining relative concentrations. If one is willing to
use Lewis' terms he would be more precise to speak of the hydro-

STANDARDIZATION OF pH MEASUREMENTS 279

gen electrode method as a means of determining relative hydrogen
ion activities.

We may note at this point that if we adopt the activity con-
cept and if we refer electrode potential differences to that of the
normal hydrogen electrode, confusion is introduced by the use
of the term normal concentration in the definition of the normal
hydrogen electrode. This is clarified if we adopt the definition
of Lewis and .Randall: "A solution is said to be at (hypothet-
ical) molar concentration with respect to hydrogen ion when the
activity of hydrogen ion in this solution is n times as great as in
1/n M solution of hydrogen ion, where n is a large number." |

The use of the equation given above instead of the equation
involving concentrations only shifts our immediate ' problem to
a new position. We are still concerned with a ratio and must
somehow establish a point of reference. At first sight we have
also shifted to a position from which it is difficult to obtain any
connection with weights of materials (concentrations).

A formal relation between activity and concentration may be set up
by the use of the socalled activity coefficient. Of this Lewis and Randall
(1921) state: ' The term activity coefficient has been used in two senses,
sometimes to mean the ion activity divided by the assumed ion molality,
and sometimes to express the ion activity divided by the gross molality
of the electrolyte."

Now, if we have a solution of HC1 so dilute that we may assume
the activity of the hydrogen ion equal to the concentration,
and if at the same time the solution is so dilute that we may assume
complete ionization, we have a starting point, for then the hydro-
gen ion activity may be determined from the analytical concen-
tration of the HC1. By the use of the electromotive force equation
relating activities we can establish by experiment the relative
activity of the hydrogen ion in a more concentrated solution.
But there is little assurance that such measurements of relative
ictivity have been made with the highest accuracy because of
he experimental and theoretical difficulties of liquid junction
Dotential differences.

By means of conductivity some idea is obtained of ion concentrations
nd by means of activity coefficients activity and concentration are

280 THE DETERMINATION OF HYDROGEN IONS

related. But since exact treatment of the subject necessitates discussion
of assumptions the reader is referred to the original literature.

Using the most probable values for the corrected degree of
dissociation of hydrochloric acid solutions, the E. M. F. of the
cell: normal calomel electrode-hydrogen electrode in N/10 or
N/100 HC1, and the estimated contact potential difference at the
liquid juncture, Lewis and Randall obtained the value 0.2776 for
the difference of potential between the normal calomel and the
normal hydrogen electrodes at 25°. This value was revised to
0.2828 by Lewis, Brighton and Sebastian (1917). Direct compari-
son with N/10 KC1 calomel electrode, as will be noted later, gave
0.3357 as the potential value of this electrode including a slight
liquid junction potential difference.

Now let us consider the values hitherto used in biochemical
work.

In S0rensen's work, published prior to the adoption of the pres-
ent standard value of the Weston standard cell, the basis for the
particular cell whose value he gave was not stated. If it was the
1.01863 used in Germany prior to 1911 the correction of S0ren-
sen's data to the present international volt will not be significant.
Doubtless the international standard was used in Denmark when
S0rensen (1912) published the summary of the data of S0rensen
and Koefoed. Their values involve two assumptions; first that
liquid junction potential differences were eliminated by the Bjer-
rum extrapolation; second, that in the calculation of the theoreti-
cal difference of potential between the normal hydrogen electrode
and the hydrogen electrode in the hydrochloric acid solutions
used, the correct hydrogen ion concentration was given by con-
ductance data. As already stated there is serious doubt of the
validity of the last assumption. Even so we ought, by using the
same degree of dissociation for hydrochloric acid solutions, to
reconcile S0rensen's value with that of Lewis, Brighton and Se-
bastian. S0rensen assumed 91.7 per cent dissociation of 0.1m
HC1 at 18°C. Employing the same value at 25°, as an approxima-
tion, we would find that the hydrogen electrode in 0.1m HC1
should be 0.0614 volts more negative than a "normal" hydrogen
electrode. If however we take "the corrected concentration of
H+ in 0.1m HC1 as 0.0816" (Lewis, Brighton and Sebastian) then
the difference would be 0.0643. The correction 0.0029 should

STANDARDIZATION OF pH MEASUREMENTS 281

bring S0rensen's value into harmony with that of Lewis, Brighton
and Sebastian. However, they are:

Lewis, Brighton and Sebastian 0.3357

S0rensen (corr.) 0 . 3347

The discrepancy of 0.0010 volt remains to be explained. That it
may be ascribed partly to an involved potential difference be-
tween N/10 KC1 and N/1 KC1 which has not been noted in the
discussion and partly to an excess correction for diffusion poten-
tial through the use of the Bjerrum extrapolation seems prob-
able from the treatment accorded this subject by Fales and
Vosburgh; but if we attempt to correct S0rensen's data by the
use of the curves given by Fales and Vosburgh the discrepancy
noted above widens. It is of no particular importance to attempt
further to reconcile the two values because S0rensen's original
data (1909) show wide variations in the E. M. F.s. of the chains
in which hydrochloric acid was used. One might therefore jump
to the conclusion that S0rensen's value is unworthy of further
consideration now that we have a more probable value. It must
be emphasized however that we are not so much concerned with the
reliability of S0rensen's original data as we are with the fact that
the value thereby assigned to the tenth normal calomel electrode
has been widely used in the study of hydrogen electrodes in solu-
tions which exhibit comparatively low diffusion potentials against
KC1 and which furnish hydrogen electrode potentials reproducible
with a considerable degree of precision. Because of this, because
of the fact that the S0rensen value and other comparable values
have standardized an enormous amount of biochemical data we
regard it as important to consider the old value further.

When S0rensen's value has not been used directly it has been
used indirectly in the taking over of pH values assigned to standard
solutions such as standard acetate. In Walpole's study of acetate
mixtures he appears to have been consistent in using the value
assigned by S0rensen to the tenth normal calomel electrode referred
to the normal hydrogen electrode under one atmosphere of hydro-
gen plus vapor pressure. He obtained a value for the hydrogen
electrode potential in standard acetate agreeing with that found by
S0rensen and by Michaelis. In Clark and Lubs' study of phthal-
ate, phosphate and borate buffer mixtures they applied the Bjer-

282 THE DETERMINATION OF HYDROGEN IONS

rum extrapolation, and, with the qualifications stated in their
paper reached a value1 for their tenth normal calomel electrode
in substantial agreement with S0rensen's.

Palitzsch doubtless used the S0rensen value, which he originally
aided in determining, in his study of borate buffer mixtures.

A variety of similar channels might be followed to, show that
in the biochemical literature there is substantial agreement so far
as the assumed difference between the tenth normal calomel and
the normal hydrogen electrodes is concerned. Since the liquid
junction potential differences between saturated KC1 and the
buffer solutions and physiological fluids dealt with in biochemis-
try are of a low order of magnitude it seems fair to assume that
the more precise biochemical data are fairly well standardized,
though not necessarily accurate. The agreement was further-
more encouraged in other lines of investigation by the
recommendation of Auerbach (1912) when, in his summary of
the work of the "Potential Commission," he recommended the
use of the tenth normal calomel as a working standard because
of its low temperature coefficient, and assigned the value 0.337
for use between 20° and 30°.

On the one hand, then, we have what may be regarded as a
tacitly accepted and not yet precisely formulated standardization
of the tenth normal calomel electrode; and on the other hand a
distinctly different value for the tenth normal calomel electrode
that is doubtless more nearly correct, though the details by which
the value was reached are not presented. The biochemist is thus
placed in an' embarrassing position. Before making a choice he
may consider the present situation in our knowledge of the tem-
perature coefficients of calomel electrodes.

In dealing with the temperature coefficients it will be distinctly
understood that we are not concerned with the temperature co-
efficient of the absolute difference of potential between mercury
and solution but rather with the temperature coefficient of the
calomel electrode in the cell: calomel electrode-normal hydrogen

1 Clark and Lubs give their E. M. F.'s reduced to refer to the normal
hydrogen electrode under a standard hydrogen concentration rather than
the standard pressure usually used. Since the calomel values were also
referred to the same basis the pH values given by these authors remain as
if the customary procedure had been followed.

STANDAHDIZATION OF pH MEASUREMENTS

283

electrode, when the potential difference at the normal hydrogen
electrode is defined to be zero at all temperatures. Unfortunately
we have little data upon this temperature coefficient which are
both accurate and extensive. Therefore one who chooses to take
over the better value for the tenth normal or the normal calomel
electrode will still be left in the predicament of not knowing the
precise value to use at temperatures other than 25°C.

We can only reach approximate values in the following manner
and compare the results with comparatively old experimental data.

Lewis and Randall (1914) have derived a provisional tempera-
ture coefficient for the normal calomel electrode which indicates
that the values are not a linear function of the temperature. The
derivation of these authors as applied to the tenth normal elec-
trode will be followed, but some new values obtained since the
writing of their paper will be introduced.

For the cell

PtH,

HC1
0.1 M

Hg2Cl2 Hg

Lewis and Randall give the empirical equation

E = 0.0964 + 0.001881T - 0.000,00290^

whence

dE/dT = 0.001881 - 0.00000580T

For present purposes this conforms closely enough with Ellis'
(1916) data.
It is now assumed that the temperature coefficient of the cell

will apply to

PtH,

PtH2

HC1
0.1 M

Hg5

H(
0.1

31
M

K
0.1

CI
M

Hg2Cl2 Hg

if the tenth molar hydrochloric acid calomel cell has the same
potential as the tenth molar KC1 calomel cell. Compare however
Lewis, Brighton and Sebastian (1917) who give 0.0012, and Mac-
Innes (1919) who gives 0.0.

284 THE DETERMINATION OF HYDROGEN IONS

For the cell

PtH2

HC1
0.1 M

H+|PtH2
M

For the cell

Hg Hg2Cl2

KC1

0.1 M

1.0 M

Lewis, Brighton and Sebastian give 0.0644. Assuming that in
this cell the E. M. F. is proportional to the absolute temperature,

3^, = 0.00022. Hence for the tenth molar KC1 calomel electrode
ul

against the normal hydrogen electrode

-45 = 0.00166 - 0.00000580T.
dT

Hg2Cl2 Hg

the author finds at 20° 0.0519, and at 30° 0.0536. Interpolation
between these values on the assumption that the E. M. F. is a
linear function of the temperature gives an E. M. F. at 25° which
is within 0.15 millivolts of that found by Lewis, Brighton and Se-
bastian, and a linear temperature coefficient of 0.000,17. Sauer's
value at 18° is 0.0514 and that of Fales and Vosburgh at 25° is
0.0524. Neither of these values falls in with those mentioned
above but when taken by themselves and with the 15° value,
0.0509, given in the footnote of the paper by Fales and Vos-
burgh (1918) they furnish a temperature coefficient of the same
order.

With these data we can start from the value 0.2828 as that of
the normal calomel electrode (Lewis, Brighton and Sebastian,
1917) at 25°; or with S0rensen's (1912) value, 0.3380, for the tenth
normal calomel electrode at 18° and treating each set separately
we reach the comparisons shown in table 49.

Bjerrum's values at 0°, 25° and 75° do not fit in with the calcu-
lations given above.

The values given above are admittedly uncertain and are to be
regarded as provisional in lieu of the experimental data that is
needed. It may be emphasized however that there is good reason
to believe that the temperature coefficient for the tenth normal
electrode is much lower than that of the normal calomel electrode.

STANDARDIZATION OF pH MEASUREMENTS

285

Since we can as yet only make a good guess of the temperature
relations it seems wise to choose as a standard the calomel elec-
trode with the smaller temperature coefficient and thus lower one
chance of error. This fortunately has been, for the most part,
the practice in biochemical work although it runs counter to pref-
erences which will not be discussed.

TABLE 49

LEWIS

TENTH
AGAINST
NORMAL
CALOMEL

S0RENSEN

1.0 N

0.1 N

1.0 N

0.1 N

0.1 N
Found

0.2844

^-0.3360

0.0516

0.2864

<-0.3380

0.3380

0.2840

<-0.3359

0.0519.

0.2860

<-0.3379

0.3378

0.2828

— >0.3356

0.0528

0.2S48

<— 0.3376
I

0.2817

«-0.3353

0.0536

0.2836

<-0.3372

0.3370

37.5

0 . 3364

0 3360

0.3359

0 3341

0.3344

0.3317

0.3321

Approximate temperature coefficient of normal calomel electrode
-0.000,23.

Approximate temperature coefficient of tenth normal calomel electrode
-0.000,06.

Let us then assume that this half cell, the tenth normal calomel
electrode, is to be the standard to which all working electrodes
are to be referred and let us consider finally the choice of values to
be assigned.

At 25°C. the difference between the values for the tenth nor-
mal calomel electrode given in table 49 is 2 millivolts. A change
of this amount would shift the values in the pH scale 0.03 unit pH.
This is quite insignificant or within the experimental error in many
biochemical studies. For certain purposes it is not insignificant.
When carried into mass action relations it might be serious but
in such relations there are generally involved data taken over from
conductance measurements. In such a situation therefore there

286 THE DETERMINATION OF HYDROGEN IONS

are involved complexities which are by no means covered by the
mere selection of a more probable value for the standard electrode.

We have already mentioned the fact that even if the value of
Lewis, Brighton and Sebastian be absolutely correct at 25° we
cannot assign accurately known values at temperatures other
than 25°, and we have noted the more or less tacit assumption of
standard values for various temperatures in the course of the
development of biochemical applications.

In addition to the difficulties mentioned above there is a funda-
mental question which runs throughout all present-day calcu- .
lations. As we have reiterated, all hydrogen electrode measure-
ments are referred by one route or another to some experimental
standard and the hydrogen ipn concentration or hydrogen ion
activity, as the case may be, is estimated for this experimental
standard by the use of theory which at present is in a state of
flux. One's inclination is to accept the latest value advocated
by the most advanced thought and yet it is an open question
whether the inherent relativity of the whole subject will not force
us ultimately to adopt an arbitrary standard. While certain
.investigators are accepting the value for the normal calomel elec-
trode given by Lewis, Brighton, and Sebastian, Bjerrum is apply-
ing the theory of complete dissociation of salts and reaching a
very different value. In the author's opinion it will be wise
during the present transition period to adopt a provisional
standard and in lieu of agreement reached in convention to let
that standard be in harmony with that tacitly implied in the
greater body of data. The author therefore suggests that the
values in column 6 of table 49 be used as provisional stand-
ards wherever there is no definite reason to require any other
value.

We can thus preserve uniformity in pH data and not introduce
ill-considered changes which may need subsequent frequent re-
vision before the present theoretical difficulties are removed or
before the action of an international committee fixes a standard
value.

It may be objected that under such a procedure of standardiza-
tion the symbol pH loses the precise significance which has been

attached to it. It has always been defined as log — -:. If the

STANDARDIZATION OF pH MEASUREMENTS

287

"concentration chain" does not determine with precision the ratio
of two hydrogen ion concentrations but rather the ratio of two hy-
drogen ion activities, and if, in addition, we adopt a standard of
reference in the current use of the hydrogen electrode which is not
strictly true, then pH is no longer expressive of the true value of

log . We need not be concerned with the casuistry of this sit-

uation. We need only remember that the more precise uses to
which hydrogen electrode measurements may be put involve the-
oretical difficulties which we are not yet prepared in every case
to deal with accurately,2 that in the more common uses the un-
certainty is not of a serious magnitude and that it is preferable
to maintain uniformity in the manner of stating experimental
values. If we take care to put a definite and unequivocal meaning
to experimental data, relieving them as far as possible from ill-
defined presumptions, we majr be pardoned for continuing to use
in descriptive text and in approximate calculations "hydrogen
ion concentrations." When we come to exact statements they
will be found embodied in pH values of uniform experimental
derivation.

In summary then it is suggested that :

1 . The following values shall be taken as the standard differences
of potential, liquid junction potential differences being eliminated,
between a tenth normal KCl calomel electrode and a hypothetical
hydrogen electrode immersed in a solution normal with respect to
the hydrogen ions, under one atmosphere partial pressure of
hydrogen, and considered to have zero difference of potential
between electrode and solution at all temperatures.

TEMPERATURE

18°

20°

25°

30°

37.5°

40°

Potential difference. .

0.3380

0.3379

0.3376

0.3373

0.3364

0 3360

2. The standard experimental meaning of pH shall be the cor-
rected difference of potential between the hypothetical normal

2 In very many instances constants determined by conductivity methods
are employed with precise electrode measurements without any critical
examination whatever of their applicability.

288 THE DETERMINATION OF HYDROGEN IONS

hydrogen electrode and the hydrogen electrode under measure-
ment (when this difference is derived by the use of the above
values), divided by the numerical quantity 0.000,198,37 T.

3. In every case it shall be specified whether the Bjerrum ex-
trapolation with the use of 1.75n and 3.5n KC1 was used to elimi-
nate liquid junction potentials or whether saturated KC1 was used
and considered to eliminate liquid junction potentials.

There are those who will prefer to use the saturated KC1 calomel
electrode as a working standard. Its use eliminates the protec-
tive devices required to guard the tenth normal calomel electrode
against the saturated KC1 used as a liquid bridge. Michaelis
(1914) has also noted that its temperature coefficient is such that
it tends to balance the effect of fluctuations in the temperature of
a calomel electrode-hydrogen electrode chain. Though there are
involved in Michaelis' reasoning some factors which are yet un-
certain this advantage may be granted. A practical system which
embodies the merits of the saturated calomel electrode and which
meets the requirements of the standardization suggested above is
illustrated on page 183. In this system the saturated calomel elec-
trode is the working standard whose value is given by careful com-
parison at known temperatures with a set of tenth normal calomel
electrodes.

If any ultimate experimental standard other than the tenth
normal calomel electrode be used it is suggested that for the
present it be brought into harmony with the above system, which
is the system that has practically governed past measurements,
and that fundamental revision of any standard await concerted
action based upon thorough investigation of both experimental and
theoretical data.

These suggestions simply put into definite form the current
procedure with the recognition on the one hand that the precise
use of electrode data involve many theoretical difficulties and on
the other hand that the use of such data for the approximate cal-
culation of hydrogen ion concentrations had best be standardized
for the sake of uniformity in the records to be handed on to the
future.

CHAPTER XX
Supplementary Methods

When any process has been found to be controlled by the con-
centration of the hydrogen or hydroxyl ions, when the quantitative
relations have been established and contributory factors are con-
trollable, there is established a possible means of estimating the
concentration of the hydroxyl or hydrogen ions. Many such in-
stances are known. From among them a few may be chosen for
their convenience. They are spoken of here as supplementary
methods because they are superseded in general practice by indi-
cators and the hydrogen electrode. Several have historical value
because they were used in establishing the laws of electrolytic
dissociation. Others have value because they are available
either for checking the customary procedures or for determina-
tions in cases where there is reason to doubt the reliability of indi-
cator or hydrogen electrode measurements.

An instance of the procedure outlined above is the following.
Clibbens and Francis (1912) found that the decomposition of
nitrosotriacetonamine into nitrogen and phorone is a function of
the catalytic activity of hydroxyl ions. Francis and Geake (1913)
then applied the relation to the determination of hydroxyl ion
concentrations, Francis, Geake and Roche (1915) improved the
technique, and then McBain and Bolam (1918) used the method
to check their electrometric measurements of the hydrolysis of
soap solutions.

It is just in such checking that the value of these so-called sup-
plementary methods will be appreciated. But, since they will find
only occasional use and under circumstances which will require a
detailed consideration of their particular applicability, there
seems to be no reason to do more than indicate a few of the methods
in brief outline.

THE QUINHYDRONE ELECTRODE

We have already seen in Chapter XVI that, when pH is less
than about 7, a platinum electrode in the presence of hydroqui-

289

290 THE DETERMINATION OF HYDROGEN IONS

none and quinone should show a potential difference, which,
when referred to the normal hydrogen electrode as a standard
may be expressed by the equation

RT , RT [Sdl

Eh = Ek + ~y In [H+] - ^ In jg-j (66)

where Eh is the observed single electrode potential difference,
Etis a constant and [Sd] and [Sq] are the total concentrations of
hydroquinone and quinone respectively. We have also previously
noted that, under the limitations specified, Eh becomes a linear

rs i

function of pH when the ratio — ; is kept constant and the tem-

[bqj

perature is constant. (At 30°C, for instance, — In [H+] is

- 0.06 pH.).

Now quinone and hydroquinone combine in equimolecular
proportions to form quinhydrone. (To distinguish this product
from similar compounds such as that formed from toluenequinone
and toluenehydroquinone it may be called benzoquinhydrone.)
In aqueous solutions the reaction is reversible,

quinone + hydroquinone ^ quinhydrone

and since the solubilities are low, the addition of solid quinhy-
drone is a convenient way of providing a solution with a mixture
of quinone and hydroquinone. We must be careful, however, not
to assume that the two are necessarily present in equimolecular
concentrations. We may assume that the solid quinhydrone
maintains a constant concentration of undissociated quinhydrone
in solution. This dissociates and we have the equilibrium condi-
tion where D represents hydroquinone, Q quinone and QD quin-
hydrone:

[Q][D]

[QD]

= Ki, and since [QD] is constant,

[Q][D] = KB, where K8 is the so-called solubility product.
From this it is evident that only the product [QJ[D] is kept con-
stant. Ionization of D (hydroquinone) is certainly of funda-
mental importance as outlined in Chapter XVI and we therefore
cannot neglect to consider its effect in the above equation. But

SUPPLEMENTARY METHODS 291

we have already brought the electrode potential equation into
such a form and simplified it with the assumption that it is to
be used in the region of inappreciable dissociation of D so that
we are able at once to say that the very slight ionization of the

rs i

hydroquinone (D) will not appreciably alter the ratio — — : from

IpqJ.

unity. Thus in acid solutions the presence of solid quinhydrone
maintains a practically constant, unit ratio of its dissociation
products. The last term in equation (66) becomes zero, and
we have

Eh = Ek - 0.000.198 T pH (67)

When Ek has been established a measurement of Eh enables
one to calculate pH.

Biilmann (1920) and Biilmann and Lund (1921) have devel-
oped the "quinhydrone electrode" for practical use and employ
the above equation, derived, however, in another way (assuming
the electrode to function as an actual hydrogen electrode. See
Chapter XVI).

For the preparation of quinhydrone Biilmann (1921) employed
the method of Valeur. Later Biilman and Lund (1921) found
it practicable to prepare the quinhydrone as follows:

One hundred grams of ferric ammonium alum in 300 cc. water
at 65°C. is turned into a warm solution of hydroquinone in 300
cc. water. The quinhydrone precipitates as fine needles. Cool
the mixture in ice and then filter with suction washing the needles
three or four times with cold distilled water. Yield, 15 to 16
grams. It is stated that the trace of iron remaining after this
process is without serious effect.

To form a "quinhydrone electrode" Biilmann employs a vessel
similar to those used for calomel electrodes but with a fairly
large platinum electrode (blank platinum). A little quinhydrone
is mixed with the acid solution under examination, placed in
the vessel with the platinum electrode and connected with a
saturated or other calomel electrode.

Biilmann determined Ek in equation (67) by simply fixing the
pH at a known value with definite buffer solutions and measuring
:he difference of potential between a quinhydrone electrode in

292 THE DETERMINATION OF HYDROGEN IONS

this solution and a hydrogen electrode in the same buffer without
quinhydrone. He gives:

Temperature

0.704

0.699

Besides the benzoquinhydrone electrode Biilmann also describes
electrodes formed with the xylene and toluene homologues.

Biilmann and Lund describe capillary vessels for use with
such electrodes.

S0rensen, S0rensen and Linderstr0m-Lang (1921) discovered
that there is a "salt error" with the quinhydrone electrode which
becomes very appreciable at salt concentrations of the order of
M/5. This they ascribe to an altering ratio of activities for the
quinone and hydroquinone with change in salt content.

By methods for the detail of which the reader is referred to
the original papers it is predicted that the ratio of the activities
of hydroquinone and quinone is defined when the solution is
saturated with quinhydrone and one of the components, hydro-
quinone or quinone; and that under these circumstances there
should be less "salt error." There may then be formed what
Biilmann and Lund call the hydro-quinhydrone electrode and the
quino-quinhydrone electrode.

The hydro-quinhydrone electrode is similar to the quinhydrone
electrode described above except that there is present besides
solid quinhydrone, solid hydroquinone. At 18°C. the Ek value
of this electrode is given by Biilmann and Lund as 0.618.

In the quino-quinhydrone electrode there is present besides
solid quinhydrone, solid quinone. At 18°C. the Ek value of this
electrode is 0.756. In each case the platinum of these electrodes
is positive to the platinum of the hydrogen electrode by the given
values.

There are a number of details in the use of these electrodes
which require further study and the reader is referred to the orig-
inal literature for those which hrve already received attention.

Aside from the great interest of the subject as an example of
the general relations pointed out in Chapter XVI the electrodes
developed by the Danish investigators should be useful in those
cases where the hydrogen of the hydrogen electrode is seriously
attacked by the components of a solution. But by the same token

SUPPLEMENTARY METHODS 293

the quinhydrone electrode cannot be used when the reduction
potential of a solution is such as to seriously alter the ratio of the
hydroquinone and quinone. In either case, however, there re-
mains the possibility of taking advantage of the slowness with
which some oxidation-reduction reactions come to equilibrium
and experience alone will indicate the limitations of usefulness.
Independently of the Danish investigations Granger and Nel-
son (1921) worked out some of the relations involved in the quin-
hydrone electrode.

CONDUCTIVITY

The conductivity of a solution is dependent upon the concen-
trations of all the ions and upon the mobilities of each. It is
therefore obvious that a somewhat detailed knowledge of the con-
stituents of a solution and of the properties of the constituents is
necessary before conductivity measurements can reveal any ac-
curate information of the hydrogen or hydroxyl ion concentra-
tion. Even when the constituents are known it is a matter of
considerable difficulty to resolve the part played by the hydrogen
ions if the solution is complex. However, the mobilities of the
hydrogen and hydroxyl ions are so much greater than those of
other ions (see page 163) that methods of approximation may be
based thereon. If, for instance, a solution can be neutralized
without too great a change in its composition it may happen that
with the disappearance of the greater part of the hydrogen ions
there will appear a great lowering in conductance. Then, with
the appearance of greater hydroxyl ion concentration, the conduct-
ance will rise. The minimum or a kink in the curve is
a rough indication of neutrality. Thus the conductivity method
is sometimes useful in titrations. See Kolthoff for details and
references.

The elementary principles of conductivity measurements will
be found in any standard text of physical chemistry but the more
refined theoretical and instrumental aspects are only to be found
by following the more recent journal literature.

294

THE DETERMINATION OF HYDROGEN IONS

CATALYTIC DECOMPOSITION OF NITROSOTRIACETONAMINE

The reaction taking place is represented in outline by the
following equation :

pn/^2 * C(CH3)2\M . ma _^ nrk/CH: C(CH3)2 , v , w n
C0\CH2 • C(CH3)2/N N° "* C0\CH: C(CH3)2 + Na + Hz°

The original quantity of nitrosotriacetonamine is known and the
extent of the decomposition at the end of measured intervals of
time is measured by the volume of nitrogen evolved.

Fig. 41. Vessel for the Catalytic Decomposition op
Nitrosotriacetonamine

Francis, Geake and Roche (1915) use the vessel shown in figure
41. The tap of the reaction vessel contains a cup B of 7 to 10
cc. capacity into which the alkali or the nitrosoamine can be intro-
duced through F. The solution is then shut in by turning the key
through a right angle. The cup becomes a part of the reaction
chamber A on turning the key as shown in the figure. The ves-
sel is immersed in a thermostat and shaken during the whole ex-
periment. The holes at E and E' permit the cup B to be bathed

SUPPLEMENTARY METHODS 295

by the thermostat liquid and so reach thermal equilibrium at the
same time as the chamber A. The tube R connects with a con-
stant volume burette where the evolved nitrogen is collected and
its pressure read. The tube D is used for washing out the vessel
and for filling it with nitrogen when the reaction has to be con-
ducted in an atmosphere free from oxygen.

The unimolecular equation, using the pressure method is

k = 2'303 lo Pc° ~ P°
t °g P. - Pt

where P0 is the pressure at the time taken as zero, Pt the pressure
taken at the time t and Poo the so-called infinity reading at the
end of the experiment. The unit of time taken is the second. At

30°, — ^— = 1.92.
[OH-]

It was found that the constants obtained with nitrosotriace-
tonamine commence to drift when the ion concentration reaches
O.Oon while at 0.35n the drift ceases and the method is again
applicable. To bridge the gap it was found that nitroso-vinyl-
and isobutyl-diacetonamines could be used.

For temperature coefficients and for the influence of neutral
salts etc. the original paper may be consulted.

CATALYTIC DECOMPOSITION OF DIAZOACETIC ESTER

Bredig and Fraenkel (1905) have described the following reac-
tion as applicable to the determination of hydrogen ion concen-
trations.

N2CH.C02 C2H5 + H20 = N2 + (OH)CH2C.C02C2H5
The nitrogen evolved from time to time is measured and the
values used in the equation

1 °

k = „ dn.n , log

0.4343 t a - x

vhere a is the total gas at the end of the reaction, x the gas after

k
lme t minutes and k the reaction constant. At 25°C, ^r, = 32.5.

The method was applied with only partial success by Hober
1900) to blood. Van Dam (1908) used it in the examination of
ennet coagulation of milk.

296 THE DETERMINATION OF HYDROGEN IONS

THE INVERSION OF CANE SUGAR

This has been a favorite subject of study by those interested
in the catalytic activity of the hydrogen ion. It has been
used in a number of instances for the determination of the
hydrogen ion concentration of biochemical solutions, but, like
all catalytic processes, its close study has revealed a number of
complicating factors which necessitate the greatest caution in the
interpretation of results.

So numerous are the papers dealing with sugar hydrolysis by
acid that the reader is referred to the very thorough review by
Woker for the older work. For the more recent investigations
see, for example, Jones and Lewis, 1920.

CATALYSES IN GENERAL

Pending further development of the theory of strong electrolytes
and of the "salt effect", the investigator, using one or another
of the above catalysis methods merely as a check, can place his
data upon a reproducible basis by using the following system of
comparison. Determine the pH values of a series of buffer
solutions lying within the pH range expected of the unknown,
and having total salt concentrations comparable to that of the
solution to be tested. Under parallel conditions determine the
catalytic activity of knowns and unknown. Assume that the
result with the buffer agreeing closest to that of the unknown
indicates that this buffer and the unknown are at the same pH
and check by various modifications of buffer.

MISCELLANEOUS METHODS

Were it worth while there could be compiled under this heading
a wide variety of phenomena which have actually been used to
determine approximately the hydrogen ion concentration of a
solution. We may instance the precipitation Of casein from milk
by the acid fermentation of bacteria. This has not been clearly
distinguished in all cases from coagulation produced by rennet-
like enzymes; but, when it has been, the precipitation or non-pre-
cipitation of casein from milk cultures has served a useful purpose
in the rough classification of different degrees of acid fermentation.

SUPPLEMENTARY METHODS 297

In like manner the precipitation of uric acid or of xanthine has
been used (Wood, 1903).

The alteration of the surface tension of solutions (Windish and
Dietrich, 1919-1921), the distillation of ammonia (Vely 1905), dis-
tribution ratios between different solvents, and various other
methods have been used to furnish data for the estimation of
hydrogen or hydroxyl ion concentrations.

CHAPTER XXI

Applications

Finally, acidity and alkalinity surpass all other conditions, even
temperature and concentration of reacting substances, in the influence
which they exert upon many chemical processes. — L. J. Henderson.

It is because of the great variety of applications in research,
routine and industry that the theories and devices outlined in the
previous chapters have been developed. The physical chemist
sees in them the instruments of approximation or of precision
with which there have been discovered orderly relations of ines-
timable service to the analyst and with which there have been
established quantitative values for affinity or free energy. The bio-
chemist might almost claim some of these methods as his own, not
only because necessity has driven him to take a leading part in
their development, but also because their application has become
part of his daily routine in very many instances.

As mentioned in the preface to the first edition the applications
have become so numerous and in many cases so detailed that the
time has come for a redispersion among the several sciences of
the material that has from time to time been grouped about the
activity of the hydrogen ion. This chapter therefore is written
only as a cursory review with the hope that it may be of service
to the student by revealing the interdependence of specialized
lines of research, by suggesting how mistakes still current have
been eliminated by those who realize the importance of the sub-
ject and by furnishing a rough index to our incomplete bibliog-
raphy of a voluminous literature.

In the compilation of the bibliography, of which this chapter
constitutes an index, no attempt has been made to include all of
the very numerous instances in which the activity of the hydrogen
or the hydroxyl ions has been found to influence the course of spe-
cific chemical reactions, such as the hydrolysis of polysaccharides,
special oxidations and condensations, or the nature and accuracy
of the numerous color tests used for the qualitative recognition of
special chemical groupings. The reader will find in Woker's ex-

298

APPLICATIONS 299

tensive monograph, Die Katalyse, not only a very complete re-
view of the older, widely scattered literature upon these aspects
of hydrogen and hydroxyl ion activity but also an abundance of
material which still remains to be reworked with the more modern
methods.

In the classification of the bibliography no attempt has been
made to place the references in strictly logical catagories, nor
has it been practical to make a minute subdivision by subjects
with numerous cross references. The grouping is by subjects
which are of particular current or historical interest or which
fall within the provinces of special branches of science.

General Reviews. Excellent general reviews of biochemical
applications are S0rensen's article in Ergebnisse der Physiologie,
1912, and MichaekV monograph Die W asserstoffionenkonzentra-
tion, 1914. As we go to press there comes to hand the first part
of the 1922 revised edition of this excellent monograph. This
first part covers in extended form the theoretical foundations
briefly treated in the first edition and deals in more- or less detail
with many subjects briefly touched upon in the following pages.
Prideaux has compiled a great deal of valuable data in The Theory
and Use of Indicators, London, 1917. In this English work will
be found the more important matter which Bjerrum (1914)
embodied in his monograph on the theory of titration and which
Noyes had previously summarized in his paper "Quantitative
application of the theory of indicators to volumetric analysis,"
(1910). The analyst will find a wealth of helpful suggestions in
Stieglitz' Qualitative Analysis. A review of the indicator method
which is of some general interest, although written specially for
the bacteriologist, will be found in The Journal of Bacteriology,
2, nos. 1, 2 and 3 (Clark and Lubs, 1917).

Those who desire to review the theory of electrolytic dissociation
with special reference to its bearing on electrode measurements
will find useful LeBlanc's Text Book of Electrochemistry (1907).

Among several papers which may be called classics in biochem-
istry there will be recognized the preeminence of S0rensen's Etudes
enzymatiques, II, from the Carlsberg Laboratory in Copenhagen
and Das Gleichgewicht zwischen Basen und Sduren im tierischen
Organismus by Henderson of Harvard.

The Theory of Titration is so closely allied with the more

300 THE DETERMINATION OF HYDROGEN IONS

general applications of indicators and the hydrogen electrode that
it may well be taken from the alphabetic arrangement to be fol-
lowed and treated before taking up some general considerations.

The stress which has come to be laid upon that factor of "acid-
ity" with which we have been dealing should not detract from the
true importance of the estimation of total acidity or alkalinity by
titration.

But the theory of titration is only a special form of the theory
with which we have been concerned up to this point; so that we
are prepared to sketch in outline those salient features of the well-
ordered theory which has displaced the loose empiricism of other
days.

In figure 42 are shown the titration curves of hydrochloric,
acetic and boric acids, determined as outlined in Chapter II. The
ordinates of figure 42 are pH values and the abscissas cubic centi-
meters of N/10 NaOH added to 10 cc. N/10 acid. At the side
of the main part of the figure are representations of the color trans-
formations of two indicators (see Chapter IV).

Although the indicator curves are drawn at one side of the figure
the reader will readily see from the theory described in Chapter
IV that they could have been placed in the main figure parallel
to the titration curves if the abscissas had been made percentage
neutralization.

A more complete picture of the conditions of titration would
be shown had the curves been extended to indicate what happens
when the "end-points" are overstepped. The reader may pic-
ture this for himself by imagining that the curve for boric acid
continues with the slope shown at 11 and then flattens out be-
tween 12 and 13, and that the other curves, after passing pH 10,
sweep to the right to join the extended boric curve.

When all but a very small part of the hydrochloric acid has been
neutralized there comes a sharp break in the titration curve. On
the addition of the last trace of alkali required for complete neu-
tralization the pH of the solution plunges to the alkaline region.
In this precipitous change the pH passes the range of methyl red,
and, with an amount of alkali that will be detected only by careful
observation, it passes into that range of pH where phenolphthalein
shows its various degrees of color. Therefore, with the exclusion
of carbon dioxid, either indicator may be used to indicate the "end

APPLICATIONS

301

point" of this titration. The case is very different in the titration
of acetic acid. Here we have an acid whose dissociation constant
(see Chapter I) is so low that the flat portion of the titration curve
lies in that region of pH where methyl red shows its various de-

2
3

•

^CV

5
6

10
pH

^<^c

4£rr>

4£*d

I A

1. t

> I

i 1

Fig. 42. Titration Curves of 10 cc. N/10 Acids with N/10 NaOII

302 THE DETERMINATION OF HYDROGEN IONS

grees of color. In other words the apparent dissociation constant
of methyl red is not far from that of acetic acid. Therefore, as
the titration of acetic acid proceeds, and long before the neutraliza-
tion of the acetic acid is complete, methyl red has been partially
transformed and at last is so extensively transformed that no
marked change of color is observed when the pH of the solution
abruptly changes with complete neutralization of the acetic acid.
It is at once evident why an indicator with the properties of
phenolphthalein must be used in such a case. In the titration of
a still weaker acid, such as boric acid, phenolphthalein becomes
comparable to methyl red in the latter's conduct in acetate solu-
tions. To titrate boric acid it must be combined with glycerine
or mannitol to form a stronger acid. See Liempt (1920).

The titration curve of boric acid is representative of the conduct
of many of the weak acidic groups found in the substances of
biochemical interest.

Sometimes by a judicious selection of indicators it is possible to
titrate in succession a mixture of two acids. For instance A. B.
Clark and Lubs (1918) have called attention to the advantages of
the two color transformations of thymol blue. The color trans-
formation of thymol blue in the acid range is such that it may be
used to indicate the approximate end point of hydrochloric acid
in the presence of acetic acid ; and the second color change occurs
in a region of pH such that it will indicate the end point in the
titration of the acetic acid. A. B. Clark and Lubs (1918) and Lubs
(1920) have examined other similar uses of this indicator.

The principles thus briefly outlined apply to the titration of
bases with strong acids, but, of course, with the direction of pH
change reversed and with the end points tending to He on the acid
side of pH 7.0. A hydrogen ion concentration of 10_7n or pH 7.0
is called the neutral point because it is the concentration of both
the hydrogen and the hydroxyl ions in pure water; but it is evi-
dently seldom the practical or even the theoretical point of neu
trality for titrations.

As phenolphthalein is the more generally useful indicator for
the titration of acids with strong bases so is methyl red the more
generally useful indicator in the titration of bases with strong acids.
Each fails, however, when the acid or base is very weak, and each
may be replaced by a more suitable indicator in special cases.

APPLICATIONS 303

For the treatment of these cases the reader should consult the
detailed description of the theory of titration in one of the papers
mentioned above.

Where high color or turbidity interferes with the use of indi-
cators in titration the hydrogen electrode is often useful. See
Bottger (1897), Hildebrand (1913) Michaelis (1917). Since it
may be necessary only to detect the "break" in the titration curve,
the hydrogen electrode system and potentiometer system used for
this purpose may be very simple. The hydrogen electrode has
the advantage that it may often be used where colorimetric tests
are impracticable and that it may be linked electrically with auto-
matic regulating and recording instruments such as Leeds and
Northrup Company have devised for industrial use.

Pinkhof (1919) has suggested special half-cells with single
potentials equal to those of the end-points of titrations, thereby
eliminating the necessity of a potentiometer. A galvanometer
or electrometer indicates equalization of potentials and hence the
attainment of the "end-point."

In like manner one may use two hydrogen electrodes as de-
scribed in Chapter IX. If one electrode is immersed in a solu-
tion having the pH of the desired end-point, the attainment of
this end-point in the other solution is indicated by the point of
reversal of current in the galvanometer (Klopsteg, 1921).

Since titrimetric determination of total acidity or basicity
involves one or another method of estimating pH, the under-
standing of the principles involved is essential to an intelligent
interpretation of the values obtained in the titration of complex
mixtures. In a great many instances there have been carried
over to the titration of complex mixtures the rule-of-thumb method
and the special interpretation first worked out by the analyst for
the titration of strong acids and bases. Now it not infrequently
occurs, especially among extracts of natural products, that there
are present a variety of weak acids and bases; and no precipitous
drop in the titration curve can be observed in the pH zones covered
by the indicators very generally employed in such titrations.
The situation is comparable with an attempt to titrate boric acid
with phenolphthalein as indicator. No sharp "end-point" is
observable. But there will always remain the distinctive value
of a titration and wherever this cannot be precisely analyzed it
should be stated in simple straightforward terms.

304 THE DETERMINATION OF HYDROGEN IONS

In the majority of cases the titration of such solutions reduces to a mere
revelation of differences in total buffer action furnishing but one definite
point on the titration curve. The procedure often followed is comparable
with the practice of the ancient Romans who, according to Trillat (1916),
(cf. Stephanides 1916) titrated natural waters with drops of red wine.
While modern standards of concentration are more exact than the wine
standard of the Romans their significance is largely lost by a choice of in-
dicators as accidental as the Roman choice of the coloring matter of red
wine. The frank admission that the content of acids in some complex
solutions cannot be determined by titration need not destroy the value
of the information gained by a titration if this information be correctly
used. But too often the matter is carried to an extreme. In the routine
methods for titrating milk a perfectly simple test has been so elaborated
that it not only has become confusing to the chemist but so misleading to
the creamery man that it is causing large economic losses. Often the
initial pH of a solution is of greater significance than is the titration value
obtained after juggling the solution with acid or alkali. Illustrations of
this are to be found in the author's treatment of bacteriological culture
media (Clark, 1915).

Having followed some of the salient features of titration and
found this procedure linked with the more general aspects of hy-
drogen ion determinations the reader is reminded of those relations
among acids and bases outlined in Chapter I which point to
certain general considerations.

General Considerations. As a comprehensive generaliza-
tion it may be said that the hydrogen ion concentration of a solu-
tion influences in some degree every substance with acidic or basic
properties. When we have said this we have said that the hydro-
gen ion concentration influences the great majority of compounds,
especially those of biochemical interest. Such a generalization,
however, would be misleading if not tempered by a proper appreci-
ation of proportion. Rarely is it necessary to consider the ioniza-
tion of the sugars since their dissociation constants are cf the order
of 10~13 and their ionization may be generally neglected in the pH
region usually encountered in physiological studies. Likewise
there are zones of pH within which any given acidic or basic group
will be found in dilute solution to be in a practically undissociated
or fully dissociated state. Perhaps there is no more vivid way of
illustrating this than by a contemplation of the conduct of indi-
cators. Above a certain zone of hydrogen ion concentration
phenolphthalein solutions are colorless. Below this zone (until

APPLICATIONS 305

intense alkalinity is reached) only the colored form exists. Within
the zone the virage of a phenolphthalein solution is intimately
related to the hydrogen ion concentration. The conduct of phen-
olphthalein, which happens to be visible because of tautomeric
changes which accompanj^ dissociation, is a prototype of the con-
duct of all acids. Just as we may suppress the dissociation of
phenolphthalein by raising the hydrogen ion concentration of the
solution so may we suppress the dissociation of any acid if we can
find a more intensely ionizing acid with which to increase the hy-
drogen ion concentration of the solution. Similar relations hold
for bases, and, if we regard methyl red as a base, we may illustrate
with it the conduct of a base as we illustrated the conduct of an
acid by means of phenolphthalein.

Such illustrations may serve to emphasize the reason underly-
ing the following conclusion. Whenever, in the study of a physi-
ological process, of a step in analysis requiring pH adjustments or
of any case involving equilibria comparable with those mentioned
above, there is sought the effect of the pH of the solution, it may
be expected that no particularly profound effect will be observed
beyond a certain zone of pH. Within or at the borders of such a
zone the larger effects will be observed. From this we may con-
clude that the methods of determining hydrogen ion concentra-
tions should meet two classes of requirements. In the first place,
when the phenomenon under investigation or control involves an
equilibrium which is seriously affected by the pH of the solution,
the method of determining pH values should be the most accurate
available. In the second place, when the equilibrium is held prac-
tically constant over a wide range of pH, an approximate deter-
mination of pH is sufficient and refinement may be only a waste
of time.

Neglecting certain considerations which often have to enter into
a choice of methods it may be said that the electrometric method
had best be applied in the first case and the indicator method in
the second. When the nature of the process is not known, and it
therefore becomes impossible to tell a priori which method is to be
chosen, the colorimetric method becomes a means of exploration
and the electrometric method a means of confirmation.

Exception will be taken to this statement as comprehensive
for there are cases where one or the other method has to be

306 THE DETERMINATION OF HYDROGEN IONS

discarded because of the nature of the solution under examina-
tion. Nevertheless, in general, the utility of the colorimetric
method lies in its availability where approximations are needed and
exact determinations are useless and also in its value for recon-
naissance; while the value of the electrometric method lies in its
relative precision.

In some instances the qualitative and quantitative relations of
a phenomenon to pH should be carefully distinguished. Note, for
instance, the significance of an optimum or characterizing point.
Consider the conduct of phenol red and of cresol red. These two
indicators appear to a casual observer to be very much alike in
color and each exhibits a similar virage in buffer solutions of pH
7.6, 7.8, etc. Careful study, however, shows that each point on
the dissociation curve of phenol red lies at a lower pH than the cor-
responding point on the dissociation curve of cresol red. If the
half transformation point be taken as characteristic it may be
used to identify these two indicators. Likewise it is the dissocia-
tion constant of an acid or a base, the isoelectric point of a protein,
the optimum pH for acid agglutination of bacteria, or an optimum
for a process such as enzyme activity that furnishes characteristic
data.

When there is observed a correlation between pH and some effect,
the mere determination of pH alone will of course throw but little
light upon the real nature of the phenomenon except in rare in-
stances. Determination of the hydrogen ion concentration will
not even distinguish whether a given effect is influenced by the
hydrogen or the hydroxyl ions, nor will it always reveal whether
the influence observed is direct or indirect. It is true, however,
that, even when the hydrogen ion concentration is effective
through remote channels, it may be very important. Therefore
advantage should be taken of the comparative ease with which the
concentration of hydrogen ions may be determined or controlled
and its influence known or made a constant during the study of
any other factor which may influence a process. From this
point of view methods of determining hydrogen ion concentration
take their place beside thermometers, and buffer mixtures beside
thermostats.

Indeed it may be said that the failure to take advantage of
buffers is still a prolific source of error in the experimental work

APPLICATIONS 307

of every branch of science having to do with solutions. In one
case the neglect is gross; in another case it may be a perfectly
excusable misjudgment. A complete understanding of the
effects of the hydrogen or hydroxyl ion is very far from attainment
and those who faithfully control the pH of their solutions are
often rewarded by the most surprising results. To emphasize
this aspect we may call attention to the fact that while the disso-
ciation of glucose is quite negligible in the region of pH 7 so far
as any appreciable effect upon the displacement of other acid-
base equilibria is concerned, the converse proposition is decidedly
not negligible. A shift in pH from 7.0 to 7.4 has a very marked
influence upon the conduct of glucose in heated solutions as every
media maker knows. Nor may it be forgotten that there are many
compounds only the main dissociation constants of which have
been determined; until we know the values of secondary acidic
or basic dissociations, we have not a complete description upon
which to base judgment of the conduct of such compounds in
relation to pH.

It is the opinion of the author that altogether too much em-
phasis has been placed upon the so-called "neutral point." The
relation [H+] [OH] = Kw holds all along the scale. The equality
[H+] = [OH] or pH = pOH occurs at pH 7. This is a convenient
reference point and has been seized upon as the point of division
in our habitual ideas of "acidity" and "alkalinity." But
pH 7 is not used as the end point in titrations, it is not the neutral
point in the conduct of ampholytes or selectively adsorbing ma-
terial, and seldom is anything unique seen to happen when in a
series of experiments a solution "crosses the line."

Living cells are dependent upon the maintenance of a strictly
limited hydrogen ion concentration in their environment. The
recognition of this as a fact, independently of any theory whatever
regarding the channels of influence, has brought hydrogen ion
methods into the culture laboratory and into the garden. Accus-
tomed as we are to dealing with ponderable quantities of material
we are sometimes startled by the fact. that a cell is dependent
upon the maintenance of an environment varying between the
limits 0.000,001 and 0.000,000,01 gram hydrogen ions per liter.
Sometimes the permissible limits are even closer but the order of
magnitude remains the same. Such values, however, do not

308 THE DETERMINATION OF HYDROGEN IONS

represent entities separable from the other material present in
solution. They represent only a position of balance among rela-
tively large quantities of material containing a reserve of potential
hydrogen ions.

Now that N, the number of molecules of solute present per
litre in a molar solution, is accurately known (Millikan), it is
certain that even in a solution having a hydrogen ion normality
as low as 10-13 there are about 1010 hydrogen ions per litre. This
estimate, when taken in conjunction with the electrical charge
associated with each ion, may indicate how it is that a normality
of 10-13 H+ may be detected.

But there still remains the fact that this normality is very low
in comparison with the other material present even in distilled
water. In solutions heavily buffered at pH 13 we find the hydro-
gen electrode or an acid indicator rigidly stabilized in its conduct
and it is questioned whether this can be brought about by such
extreme relative dilutions of the hydrogen ions alone. Keller
(1921) has expressed doubt of another sort. He calls attention
to the diminutive size of the hydrogen ion (allowing for hydration)
compared with a giant protein molecule, and, picturesquely pro-
portioning the one to the other as a bacterium to a Mont Blanc,
he questions the influence upon the protein which is attributed
to the hydrogen ion.

All these are "sharp-toothed questions" which, were they
"baited with more skill, needs must catch the answer." In many
of the answers given, however, there lies an easily detected fallacy.
Our present convenient modes of formulating relations are regarded
as complete pictures of the physical facts and as such are followed
to the bitter end with disastrous results. In a previous chapter
we have attempted to broaden the outlook just a little, and have
suggested that in many cases a more complete formulation of
relations would show that as the physical effectiveness of one ion
fades out at extreme dilution other components of the solution
maintain the continuity. From this point of view even the more
extreme "calculation values" retain a definite significance.

In like manner an extreme hydrogen ion concentration may be
significant as an index of the state of an equilibrium with which
the hydrogen ion itself has little actual physical significance. Its
introduction as a component of the equilibrium is a convenient

APPLICATIONS 309

and at the same time a stoichiometrically true and mathemati-
cally correct mode of expression containing no implications re-
garding the actual physical effectiveness of a small hydrogen ion
concentration as an individual quantity separable from the other
components of a solution. At higher concentrations there can
be little doubt of the physical effectiveness of the hydrogen ions
whatever their size, or energy relative to other bodies. The
energy placed on the grid of an electron tube may be small, but
the potential of the grid may determine a large flow of energy
between filament and plate. The hydrogen ions in a solution
may be small in relative size or relative numbers, but they may
control the mobilization of a large reserve. If one seeks to go
further, perhaps to formulate a more fundamental basis, he still
has to conform to the experimental data at hand.

These data are too extensive, too detailed and altogether too
complete to admit any doubt of the pragmatic value of those
measurements we now customarily express in terms of hydrogen
ion concentration or activity. Such values do indicate definite
positions of equilibrium among important components of a solu-
tion and they have oriented relations hitherto unsuspected. But
it is by no means certain that we have attained the ultimate con-
ception of what our measurements represent in terms of mechan-
isms. Better descriptions of these we eagerly await. Scientific
thought pauses where it is convenient and leaps forward when
necessity demands; but experimental measurements remain with
whatever force skill, scope and instrumental precision give them —
requiring only reinterpretation with the enlargement of vision.

In a crude way we have attempted in a previous chapter to
give a generalized picture of oxidation-reduction relations. Here
we encounter definite experimental facts which it is sometimes
convenient to express in terms of "calculation values." It may
now fairly be asked whether these are not significant as indices
of equilibria of as much importance to the delicate adjustments
of life processes as are hydrogen ion concentrations. If the
studies so far made are prophetic there will be found not only
a profound interrelationship between hydrogen ion concentrations
and oxidation-reduction equilibria but also direct control of cer-
tain biological processes by the reduction potential of the medium.
See Gillespie (1920), Clark (1920) and Clark and Cohen (1922)

310 THE DETERMINATION OF HYDROGEN IONS

for some applications in bacteriology. See also -Chapters XVI
and XX.

Adsorption. Hydrogen and hydroxyl ions are particularly
subject to adsorption upon surfaces. Since the relative activi-
ties of these ions are especially easy to measure, methods of de-
termining pH are of great value for adsorption studies. For a
review of recent work see Michaelis (1922).

References. Lachs-Michaelis (1911), Loffler-Spiro (1919),
Michaelis (1922), Michaelis-Rona (1910, 1919, 1920), Rona-
Michaelis (1919, 1920), Tanner (1922).

Analyses. The empiricism that characterized the develop-
ment of analytical methods in the hands of Fresenius and others
left specifications for the use of mixtures of acids, such as acetic,
and their alkaline salts in many separations. These we now know
control the hydrogen ion concentration. Here and there in the
special literature are to be found the calculated hydrogen ion con-
centrations in such cases and in other cases directions which are
somewhat more precise than the customary "slightly acid" or
"slightly alkaline." More recently there has been undertaken
direct experimentation with hydrogen electrode or indicator meth-
ods. The need of further development was voiced some years ago
by Dr. Hillebrand of the Bureau of Standards when he indicated
to the Washington Chemical Society the need of a systematic in-
vestigation of all analytical methods. One type of information
urgently needed may be learned from the papers of Blum, of Fales
and Ware and of Hildebrand. Colorimetric pH measurements on
carbonate equilibria are furnishing valuable information in several
simple analytical methods. Kolthoff is working on the relation of
pH to certain oxidation-reduction titrations. Many qualitative
color reactions remain to be studied.

References. Anger (1921), Behrend (1893), Bishop-Kittredge-
Hildebrand (1922), Bogue (1922), Bottger (1897), Br0nsted (1911),
Blum (1913, 1914, 1916), Eastman-Hildebrand (1914), Fales-
Ware (1919), Garard-Sherman (1918), Haas (1916), Hanzlik
(1920), Haskins-Osgood (1920), Hildebrand (1913), Hildebrand-
Bowers (1916), Hildebrand-Harned (1912), Hopkins (1921),
Kober-Haw (1916), Kober-Sugiura (1913), Kolthoff (1919-1921),
Kolthoff-Volgelenzang (1921), Koritschoner-Morgenstern (1919),
Kramer-Green (1921), Kramer-Tisdale (1921), Liempt (1920),

APPLICATIONS 311

Lizius (1921), Marriott (1916), Mattick- Williams (1921), Menten
(1920), Oettingen (1900), . Osterhout (1918), Robinson
(1919, 1922) Robinson-Bahdemer (1922), Shohl (1922),
Sollmann (1920), Swanson-Tague (1919), Tague (1920), Till-
mans-Bohrmann (1921), Tizard-Whiston (1920), Zoller (1920).

Autolysis of tissue is governed by the activity of enzymes
which are sensitive to the concentration of hydrogen ions. As the
resultant of the activity of two types of enzymes (Dernby) auto-
lysis is controlled by the pH which brings into play the activity of
each.

References. Bradley (1916), Bradley-Felsher (1920), Bradley-
Taylor (1916), Dernby (1917-1918), Gibson-Umbreit-Bradley
(1921), Koehler-Severinghaus-Bradley (1922), Morse, M. (1916-
1917).

Bacteriology. A review of the applications in bacteriology
up to 1917 is given by Clark and Lubs (1917).

Adjustment of the reaction of media by the old titrimetric proce-
dure was criticised by Clark (1915), and, on the introduction of suit-
able indicators and the evidence for the advantage of adjusting
on the pH basis, the titrimetric method has been abandoned for
more significant and easier modern methods. Studies on growth
optima (which see below) have shown that for the cultivation of
most saprophytes approximate indicator control without the use
of standards is sufficient (see Chapter VIII) . For special purposes
and especially for the study of certain important pathogens it is
well to adjust with the precision attained with standards. Seldom
is electrometric control necessary.

References. Adam (1921), Baldwin (1919), Barthel (1918-20),
(1920), Bovie (1915), Clark (1915), Clark-Lubs (1916), Conn
(1919), Cox-Wood (1920), Davis (1920), Dernby (1919), Fennei-
Fisher (1919), Foster-Randall (1921), Graoe-Highberger (1920),
Henderson-Webster (1907), Hurwitz-Meyer-Ostenberg (1915—
1916), Jones (1919), Kligler (1917-1918), Kligler-Defandorf (1918),
Ktister (1921), Mclntosh-Smart (1920), Massink (1921), Medical
Research Committee (1919), Michaelis (1921), Norton (1919),
Ponselle (1920), Reitstotter (1920), Stickdorn (1922), Wolf-
Shunk (1921).

The optimal zones and the limits of growth and general metabolism
have naturally been the chief interest in the first surveys of the

312 THE DETERMINATION OF HYDROGEN IONS

influence of hydrogen ion concentration upon bacterial activity.
It is now clear that in the future more exact studies will have to
differentiate between optimal initial pH, optimal zones of growth,
optimal zones for general or special metabolism, optimal zones
for preservation, etc. The self limitation of acid fermentation,
first clearly defined by Michaelis and Marcora (1912), has been
applied to certain practical tests; for example see Clark (1915),
Avery and Cullen (1919). pH limits for special organisms which
have commercial significance are exemplified by control of "rope"
in bread (Cohn-Walbach-Henderson-Cathcart) and "scab" on
potatoes (Gillespie-Hurst).

References. Adam (1921), Allen (1919), Avery-Cullen (1919),
Ayers (1916), Ayers-Johnson-Davis (1918), Barthel (1918),
Barthel-Sandberg (1919), Beckwith (1920), Bengtson (1922),
Boas (1920), Boas-Leberle (1918), Brown-Orcutt (1920), Bunker
(1919), Chambers (1920), Cheplin-Rettger (1920), Clark (1915-
18) Clark-Lubs (1915-1917), Cohen-Clark (1919), Cohn-Wal-
bach-Henderson-Cathcart (1918), Cole-Onslow (1916), Cole-
Lloyd (1917), Colebrook (1920), Cullen-Chesney (1918), v. Dam
(1918), Dernby, (1921), Dernby-Avery (1918), Dernby-Blanc
(1921), De Kruif (1922), Duggar-Severy-Schmitz (1917), Erick-
son-Albert (1922), Euler-Emberg (1919), Euler-Heintze (1919),
Evans (1918), Foster (1920-1921), Freear-Venn (1920), Fred-
Davenport (1918), Frothingham (1917-1918), Gainey (1918),
Gates (1919), Gillespie (1918), Gillespie-Hurst (1918), Grace-
Highberger (1920), Hagglund (1915), Hall-Fraser (1921-1922),
Henderson (1918), Holm-Sherman (1921-1922), Huddleson (1921),
Itano (1916), Itano-Neill (1919), Itano-Neill-Garvey (1920),
Johannessohn (1912), Johansen (1920), Jones (1920), Kiesel
(1913), Kligler (1918), Kligler-Robertson (1922), Kohman (1919),
Kniep (1906), Lazarus (1908), Levine (1920), Lord (1919),
Lord-Nye (1919), Lloyd (1916), Luers (1914), Meacham (1918),
Mellon (1921), Meyerhof (1916-1917), Michaelis-Marcora (1912),
Scheer (1921), Schoenholz-Meyer (1919-1921), Shaw-Mackenzie
(1918), Sherman (1921), Shohl-Janney (1917), Somogyi (1921),
Steinberg (1919), Svanberg (1918-21), Swartz (1920) Swartz-
Shohl-Davis (1921), Waksman (1918), Waksman-Joffe (1920-
21), Williams-Povitzky (1921), Winslow-Kligler-Rothberg (1919)
Wolf (1918), Wolf-Foster (1921) Wolf-Harris (1917), Wolf-

APPLICATIONS 313

Shunk (1921), Wolf-Telfer (1917), Wright (1917), Zeller-Schmitz
(1919).

The influence of pH upon bacterial metabolism. The reaction
of the medium even within the zone of optimal bacterial growth
is found to influence either the rate, or the relative rate of specific
types of metabolism. Not only the activity but also the pro-
duction of enzymes is influenced and the production of special
products such as toxins is partially controlled by the pH of the
medium.

References.. Arzberger-Peterson-Fred (1920), Avery-Cullen
(1920), Atkin (1911), Barthel (1921), Barthel-Bengtsson (1920),
Barthel-Sandberg (1920), Blanc-Pozerski (1920), Boas (1919),
Bronfenbrenner-Schlesinger (1918), Brooks (1921), Bunker (1919),
Charpentier (1921), Clark (1920), Cook-Mix-Culvyhouse (1921),
Davis (1918, 1920), Dernby-Aleander (1921), Dernby-Blanc
(1921), Dernby-David (1921), Euler-Blix (1919), Euler-Emberg
(1919), Euler-Hammarsten (1916), Euler-Svanberg (1918, 1919),
Fred-Peterson (1920), Gaarder-Hagem (1920-1921), Green (1918),
Groer (1912) Gustafson (1920), Itano (1916), Jacoby (1918),
Jones (1920), Lord-Nye (1919), Meyerhof (1917), Neuberg-Hirsch
(1919), Northrop-Ash-Senior (1919), Patty (1921), Peterson-
Fred-Verhulst (1921), Robinson-Meader (1920), Sasaki (1917),
Stevens-Koser (1920), Venn (1920), Waksman-Joffe (1921),
Wolf (1920), Wyeth (1919).

Disinfectant action of acids and bases is certainly in large meas-
ure a function of hydrogen or hydroxyl ion concentration; but
specific effects of certain acids and bases, which were suspected
before, have now been more clearly demonstrated by the use of
hydrogen ion methods. With the conductivity method Winslow
and Lochridge were able to show the effect of the hydrogen ion
in simple solutions and predicted relations which more powerful
methods have extended to complex media.

Cohen (1922) has reviewed certain relations between pH and
viability of bacteria under sub-lethal conditions. Time, tempera-
ture, and pH are now linked as controlling factors in canning.

The more direct action of hydrogen ion concentration upon
cells must be distinguished from its control upon the effective
state of a toxic compound. Knowledge of pH effects is therefore
essential to the assay of disinfectants and to the advancement of
chemotherapy.

314 THE DETERMINATION OF HYDROGEN IONS

References. Aubel (1920), Bettinger-Delaval (1920), Bial
(1902), Bigelow (1921), Bigelow-Cathcart (1921), Bigelow-Esty
(1920), Browning-Gulbransen (1921), Browning-Gulbransen-
Kennaway (1919), Clark, J. F. (1899), Clark-Lubs (1917), Cohen
(1922), Cohen-Clark (1919), Donk (1920), Friedenthal (1919),
Kronig-Paul (1897), McClelland-Waas (1922), Mliller (1921),
Neilson-Meyer (1921), Norton-Hsu (1916), Paul-Birstein-Reuss
(1910), Paul-Kr6nig (1896), Rideal-Evans (1921), Shohl-Deming
(1921), Tawara (1921), .Traube-Somogyi (1921), Vermast (1921),
Waterman (1915), Weiss (1921), Winslow-Lochridge (1906),
Wolf-Foster (1921), Wright (1917). See also "Pharmacology."

Acid agglutination of bacteria, first definitely recognized by
Michaelis (1911) in its relation to hydrogen ion concentration, has
been found to be of some diagnostic use. The discovery by Ark-
wright of separately agglutinable constituents opened up some
investigations of possibly wide bearing. Buchanan has indicated
some of the possible relations to serum agglutination.

References. Arkwright (1914), Bach (1920), Barendrecht
(1901), Bechhold (1904), Beintker (1912), Beniasch (1912),
Bergey (1912), Bondorf (1917), Buchanan (1919), De Kruif
(1922), Eisenberg (1919), (contains review and bibliography),
Field-Teague (1907), Georgi (1919) Gieszczykiewicz (1916),
Gillespie (1914), Grote (1913-1914), Heimann (1913), Jaffe"
(1912), Kemper (1916), Krumwiede-Pratt (1913), Tiess (1919),
Markl (1915), Michaelis (1911, 1915, 1917), Michaelis-Adler
(1914), Murray (1918), Poppe (1912), Radsma (1919), Schidor-
sky-Reim (1912), Sears (1913), Sgalitzer (1913), Tulloch (1914).

d'Herelle 'phenomenon. Gratia (1921).

Cell interior. Angerer (1920).

Testing fermentation. See various references under other head-
ings and especially Baker (1922), Chesney (1922), Clark (1915-
17), Clark-Lubs (1917), Laybourn (1920), Nichols-Wood (1922).

Balloelectricity.

Reference. Christiansen-Christiansen (1919).

Beer. As originally outlined by Pasteur the "reaction" of
wort has much to do with the brewing of beer. The control of
"disease" and of the protein material held in solution is to some
extent dependent upon pH as are the activities of the enzymes
concerned at each stage.

APPLICATIONS 315

References. Adler (1915, 1916), Emslander (1914-1919),
Leberle-Liiers>(1914), Liiers(1914),Liiers-Adler (1915), Schjerning
(1913). See also "Bacteriology," "Enzymes" and "Proteins."

Blood. The hydrogen ion concentration of the blood, while
varying slightly among normal individuals, is regulated with
remarkable constancy in any one individual in a normal environ-
ment. It never varies far from pH 7.4. Van Slyke »(1921),
places the normal variation between about 7.3 and 7.5 and the
limits compatible with life at approximately 7.0 and 7.8. Since
the bicarbonate-carbonic acid equilibrium is one of the most
important in the regulation of the blood's reaction it is convenient
to define the system in terms of this equilibrium. See " carbonate
equilibrium" for the derivation of the relation

PH = pK1 + log [H^°J

[free. COd

Inspection of the relations involving the carbonate ion CO 3
(see page 320) will show that at pH 7.4 [CO3] may be neglected
and the fixed carbon dioxid may be regarded as entirely bicar-
bonate. The extent of the bicarbonate dissociation is in doubt
but if we substitute [BHCO3], for [HC03] where B represents any
monovalent base, and modify pKi to accord with the experimental
conditions, we have

pH = 6.1 + log [BHC°3]

[free C02]

[BHCO3J -20

The ratio - -p^r--, determines pH. Normally it is about— .

[freeC02J • 1

From one point of view the blood may be regarded as a scav-
enger, burning the waste products in the tissues it perfuses, and
carrying off the final products of combustion of which C02 is one
of the most important for the acid-base equilibria under con-
sideration. With a given content of buffer in the blood the
hydrogen ion concentration would be maintained constant under
this inflow of C02 by the maintenance of a constant C02 pressure
in the lungs; but with varying buffer content the hydrogen ion
concentration could only be maintained constant by a mechan-
ism directly responsive to hydrogen ion concentration and ca-
pable of altering the C02 pressure. It seems that the respiratory

316 THE DETERMINATION OF HYDROGEN IONS

centre is thus directly responsive to the hydrogen ion concentra-
tion and by its regulation of the breathing maintains in the
alveolar air that level of C02 pressure which is in harmony with
the equilibria centered about constant pH under varying condi-
tions. Of this Haldane says: "The respiratory centre is enor-
mously more delicate as an index of change in hydrogen ion con-
centration of the blood than any existing physical or chemical
method." Clinical methods based on the measurement of the
alveolar C02 tension are now extensively used (see Van Slyke).
On the other hand, the C02 tension is but one item of a compli-
cated set of equilibria. It often becomes of importance to know
the relative proportions of the other constituents of the acid-
base equilibria. In pathological conditions the oxidative proc-
esses may be at fault and the carbonate equilibria must be
adjusted to accommodate the products of incomplete combustion
in the effort of the body to maintain constant hydrogen ion
concentration in the blood. Therefore it becomes important to
learn the relation of the C02 content to the alkaline reserve.
When this is done by gas chain or indicator titrations the hydro- /
gen electrode and indicator methods again enter the subject
from which they were to some extent displaced when it was found
that there was no particular object in studying a constant main-
tained physiologically with a degree of precision often beyond
the precision of experimental measurement.

Although it is convenient to express the acid-base equilibria
of the blood in terms of the bicarbonate system other equilibria
are of equal importance to a complete description of the mechan-
isms. In the plasma are other substances beside the carbonic
acid and bicarbonate which participate in the acid-base equilib-
rium; but the most interesting relations are found in the Donnan
equilibrium (see page 328) between the solutes of the plasma and
the material trapped within the membranes of the blood cells.
Of this material the blood pigment is the most important. When
oxidized (as oxyhemoglobin) it is more strongly acidic than
when reduced (as hemoglobin). The direct consequence is
this: when the blood pigment gives up oxygen to the tissues the
blood assumes more basic properties as a whole and is thus able
to take up more C02 for a given displacement of pH. The
converse change occurs on oxidation in the lungs, and tends to

APPLICATIONS 317

displace CO2. In this sense the blood pigment is a carrier of C02
as well as a carrier of oxygen.

Intimately connected with the regulation of the hydrogen ion
concentration of the blood are the functions of the kidneys (see
Cushny). By their action there are eliminated the non-volatile
products of metabolism, several of which are of great importance
for the acid-base equilibria of the blood. The colorimetric deter-
mination of the pH of the urine is a comparatively simple pro-
cedure which furnishes valuable data when properly connected
with other data. (See for instance Blatherwick, and the works
of Henderson, of Palmer and of Van Slyke.)

While the greatest interest has centered in the subjects briefly
mentioned above, there remain innumerable other problems of
importance. Of these there may be mentioned the relation of
the pH of the blood to the calcium-carrying power, to the activity
of various enzymes, to the permeabilities of tissue membranes, to
the activity of leucocytes, and to various reactions used in the
serum diagnosis of disease.

The student, if bewildered by the array of references given
below, will find it profitable to read the classic work of Hender-
son, Das Gleichgewicht zwischen Basen und Sduren im tierischen
Organismus. By following the papers of Van Slyke and his co-
workers the student will find reviews of various aspects of the
subject. The respiration phase so far as the older work is con-
cerned will be found in Barcroft's monograph. The later work
which includes the effects of pH is reviewed by Bayliss, Hender-
son, Parsons and others. Van Slyke's The Carbon Dioxide Carriers
of the Blood (1921) reviews the acid-base equilibria of the carbonate
in its relation to the acid-base equilibria of the hemoglobin, phos-
phate, etc.

References on acid-base equilibria of blood and related mechanisms.
See also " Urine."

1898 — Bugarszky-Tangl, Spiro-Pemsel.

1900— Hober.

1901— Rhorer.

1902— Friedenthal, Hober.

1903 — Auerbach-Friedenthal, Farkas, Farkas-Scipiades,
Fraenckel, Friedenthal, Hober, Hober-Jankowsky.

1904— Friedenthal.

318 THE DETERMINATION OF HYDROGEN IONS

1905— Foa, Pfaundler.

1906— Abel-Fiirth, Benedict, Szili.
1907 — Aggazzotti.

1908 — Henderson, Henderson-Spiro, Spiro-Henderson.

1909 — Hendnrson, Michaelis-Rona, Ringer, Robertson, Szili.

1910 — Hober, Kreibich, Robertson.

1911 — Adler-Blake, Bottazzi, Hasselbalch-Lindhard, Lob, Po-
lanyi, Schwartz-Lemberger, Skramlik, Winterstein.

1912 — Hasselbalch, Hasselblach-Lundsgaard, Lundsgaard, Mi-
chaelis-Davidoff, Quagliariello-Agostino, Quagliariello, Roily,
Salge, Sellards.

1913 — Elias-Kolb, Henderson-Palmer, Konikoff, Masel, New-
burgh-Palmer-Henderson, Palmer-Henderson, Rona-Gyorgy,
Rona-Takahashi, Salge, Snapper.

1914 — Barcroft, Blatherwick, Michaelis, Peabody, Peters,
Roily.

1915 — Begun-Herrmann-Munzer, Hasselbalch-Gammeltoft,
Henderson-Palmer, Levy-Rowntree-Marriott, Ma. de Corral,
Menten-Crile, Milroy, Momose, Palmer-Henderson, Poulton,
Wilson-Stearns-Thurlow, Winterstein.

1916— Gettler-Baker, Haldane, Hasselbalch-Lindhard, How-
land-Marriott, Hurwitz-Lucas, Levy-Rowntree, Marriott, Mc-
Clendon, McClendon-Magoon, Macleod, Reemlin-Isaacs,
Rona-Ylppo, Scott, Ylppo.

1917— Bienstock-Czaki, Cullen, Fitz-Van Slyke, Hasselbalch,
Henderson, Hober, Hooker-Wilson-Connet, Isaacs, McClendon-
Shedlov-Thomson, Milroy, Palmer-Van Slyke, Parsons, Peters,
Scott, Stillman-Van Slyke-Cullen-Fitz, Van Slyke, Van Slyke-
Cullen, Van Slyke-Stillman-Cullen.

1918— Bayliss, Goto, ■ Hasselbalch-Warburg, Henderson-
Haggard, Macleod, Macleod-Knapp, Sonne-Jarlov, Straub-
Meier, Zunz.

1919— Debenham-Poulton, Donegan-Parsons, Haggard-Hender-
son, Haskins, Irwin, Macleod, Parsons, Schloss-Harrington, Van
Slyke-Stillman-Cullen, Van Slyke-Austin-Cullen.

1920— Anon, Bayliss, Bisgaard-N0rvig, Blatherwick, Campbell-
Poulton, Collip, Collip-Backus, Coulter, Dale-Evans, Davies-Hal-
dane-Kennaway, Dragstedt, Forbes-Halverson-Schulz, Fredericia,
Grant, Goldman, Parsons, Haggard-Henderson, Hartridge, Haskins-

APPLICATIONS 319

Osgood, Henderson, L., Henderson, Y., Henderson-Haggard-
Coburn, Hills, Joffe-Poulton, v. Kapff, MacNider, Mellanby-
Thomas, Menten, Michaelis, Moore, Parsons, Parsons-Parsons,
Parsons-Parsons-Barcroft, Parsons-Shearer, Prentice-Lund-Harbo,
Priestley, Raymund, Reimann, Rieger, Suitsu, Van Slyke-
Palmer.

1921 — Barr-Peters, Bazett-Haldane, Busa, Chistoni, Collip,
Doisy-Eaton, Evans, C. L., Fleisch, Gauss, Haggard-Henderson,
Haldane, Hastings-Murray-Murray, Henderson, Hill, Jarloev,
Ma. de Corral, Means-Bock- Woodwell, Meier-Kronig, Parsons-
Parsons, Peters-Barr, Peters-Barr-Rule, Reimann-Reimann,
Reimann-Sauter, Roaf, Smith-Means-Woodwell, Trevan-Boock,
Van Slyke, Van Slyke-Stadie, Winterstein.

1922 — Barach-Means-Woodwell, Barkan-Broemser-Hahn, Cul-
len, Coulter, Doisy-Briggs-Chouke, Henderson, Hirsch-Peters,
Hirsch- Williams, Macleod, Parsons-Parsons, Williams-Swett.

Bread. In the baking of bread it is essential that the proteins,
such as glutin, which are responsible for the holding of the gas,
shall be conditioned by the proper pH. The pH may also control
the growth of the "rope" organism. The activity of yeast and
the evolution of CO2 from baking powders have relations to the
pH of the dough.

References. Bailey-Peterson (1921), Cohn-Cathcart-Hender-
son (1918), Cohn-Henderson (1918), Cohn-Walbach-Henderson-
Cathcart (1918), Freear-Venn (1920) Henderson (1918), Hen-
derson-Cohn-Cathcart-Wachman-Fenn (1919), Henderson-Fenn-
Cohn (1919), Jessen-Hansen (1911), Landenberger-Morse (1918)
(1919), Liiers (1920), Patten (1920), Sharp-Gartner (1922), Wahl
(1916).

Breeding. Control of spermatozoan activity. See "Compara-
tive and General Physiology," and C. G. L. Wolf (1921).

Body Fluids (other than blood, urine, digestive juices, cere-
brospinal fluid).

References. Aggazzotti (1921), Bloomfield-Huck (1920), Collip
(1920), Farkas-Scipjades (1903), Foa, (1905, 1906), Fraenckel
(1905), Gies (1916), Goldberger (1917), Hertel (1921), Huddelson
(1921), Lob-Higuchi (1910), Loeb-Atchley-Palmer (1922), Long-
Fenger (1915, 1916), Marshall (1915), Michaelis-Kramsztyk
(1914), Okada (1915), Quagliariello (1916-1921), Schade-Neu^
kirch-Halpert (1922), Shepard-Gies (1916), Uyeno (1919).

320

THE DETERMINATION OF HYDROGEN IONS

Canning. The National Canners' Laboratory has so related
time, temperature and pH that economy and certainty in the
commercial sterilization of canned foods can be assured.

References. Bigelow (1921), Bigelow-Cathcart (1922), Koh-
man (1922), Rogers-Deysher-Evans (1921).

Carbonate Equilibria. When carbon dioxid dissolves in
water without any base to form carbonate there are presumably
present in the water both anhydrous C02 and the hydrate,
H2CO3, carbonic acid. Analytical methods do not ordinarily dis-
tinguish these two forms, and, since the sum of the two is generally
the more important quantity, we may write the equilibrium equa-
tion for the relation between a partial pressure, P, of gaseous
carbon dioxid and the dissolved carbon dioxid as follows:

[C02] + [H2C03] = [free C02] = KoP

In the presence of bases we still have the above relation holding
tbetween the partial pressure and that portion of the total CO2
c which remains uncombined. However, variation in the composi-
tion of the solution will vary the magnitude of K0. We probably
make no significant error if we regard [free C02] in carbonate solu-
tions to be influenced by the total salt (carbonate) just as it is
influenced by the total salt concentration in a solution containing
no base. On this basis Johnston (1915) uses Bohr's data for
the absorption coefficients of carbon dioxid in sodium chlorid
solutions of different concentration, and calculates therefrom
the values of Kq in terms of molar concentration.

Johnston's table of K0

TEMPERATURE

IN WATER

IN 1 . 17 M SALT

IN 3.44M SALT

3.5

0.0672

0.0484

0.0270

4.2

0.0500

0.0367

0.0213

16.0

0.0441

0.0328

0.0193

25.0

0.0338

0.0260

0.0159

30.0

0.0297

0.0232

0.0142

40.0

0.0236

0.0185

0.0117

From these values Johnston interpolates the following values
of K0 for the indicated concentrations of total base or salt at

25°C. Included below are the values of pKo = log

Ko'

APPLICATIONS

321

TOTAL BASE
OR SALT

0.0

0.1

0.2

0.3

0.5

1.0

pK„

0.0338
1.471

0.0329
1.483

0.0321
1.493

0.0314
1.503

0.0300
1.523

0.0270
1.569

Dissolved C02 reacts with water and since [H2O] may be regarded
as constant we have the equilibrium equation

[CQ

[H2CO;

= K,Qr [CQ2l + [HsCOa] = K,+ x

[H2C03

(68)

The H2C03 dissociates in steps and for the first step the equilib-
rium condition is

[H+] [HCQ3]
[H2C03]

= K"

69)

Combining equations (68) and (69) and collecting constants we
have

[H+] [HCO3] =
[COJ + [H2C03]

or using the convention mentioned above
[H+] [HCO3]

[free C02]

= Ki

(70)

The constant Ki is sometimes called the first dissociation con-
stant of carbonic acid. It is not strictly so but is rather of the
nature of an "apparent dissociation constant." Ki is more use-
ful than the true dissociation constant but is probably much
smaller.

For the second stage of dissociation the equilibrium condition is:

[H+] [CO,]

= K2

(71)

[HCO3]

In addition to these equations there is the useful relation
)f electrical neutrality,

[B+] + [H+] = [HCOj + 2 [C03] + [OH] (72)

vhere [B+] represents the total concentration of cations other than
H+] and all species are represented in equivalent concentrations.

322 THE DETERMINATION OF HYDROGEN IONS

One of the chief experimental difficulties in handling carbonate
solutions is the control or the evaluation of P. But while this
is susceptible to management the correct evaluation of Ki and
K2 is a matter of great complexity for the following reasons. If
salts such as Na2C03 and NaHC03 are used as experimental ma-
terial to establish various proportions of carbonate and bicarbon-
ate ions it becomes necessary to know the degree of their dis-
sociation at known concentrations of the salts, or if complete
dissociation occurs it becomes necessary to know the effect of
different concentrations upon activities. This involves the whole
unsettled question of the conduct of "strong electrolytes." Hith-
erto there have been carried over to pH studies the constants
derived by the use of conductivity data which are not strictly
applicable.

If yi represents the degree of dissociation of NaHCC>3 and
y2 degree of dissociation of Na2C03 we have the following rela-
tions according to Seyler and Lloyd (1917).

[Na] 0.05 0.1 0.2 0.3 0.5 1.0

y! 0.82 0.78 0.73 0.69 0.64 0.52

y2 0.56 0.66 0.37 0.31 0.24 0.14

Space does not permit a detailed discussion of the above values
and numerous other quantities which enter into the data of
carbonate equilibria. We shall proceed with the more general
relations indicated by the pure equilibrium equations and shall
give without comment Johnston's values for the more important
constants.

Putting the equations into logarithmic form, and using for

terms such as log ^ the expression pK, we have the following
useful relations:

pH = pKi + log [HC03] - log [free C02] (73)

pH = pKi + pK0 + log [HCO3] - log P (74)

pH = pK2 + log [C03] - log [HCO3] (75)

pH = I pK0 + \ pKx + \ pK2 - \ log P + \ log [C03] (76)

m+1 J 2X0^1^ + KpKxP [H+] + Kw [H+] - [H+P

L J [H+]2 ,

For the values of pK0 see page 320. From Johnston's selected

APPLICATIONS

323

values for the first and second acid dissociation constants at
25°C. we have pKi = 6.47 and pK2 = 10;32. For other values
see references.

Inspection of the combined equations will show that pH is
denned by any two of the variables or conversely that pH and
one variable determine the state of a carbonate equilibrium.
By the use of equation (77) the total base can be brought into
consideration and it can be shown that the total base and one
variable such as pH or P will define the position of a carbonate
equilibrium. See (77). Thus a carbonate solution exposed to the
atmosphere with its more or less constant partial pressure of
C02 at 0.0003 atmosphere will tend to reach a definite pH value
which is determined by the total base. This may be as low as
pH 5.0 for solutions containing very little base or as high as pH
10 in a solution about normal with respect to [B+]. Based upon
such relations are analytical methods for determining C02 par-
tial pressures from pH and known concentrations of total base.

Equations (73) and (74) are of importance in the study of blood
the pH of which may be defined in terms of the ratio of bicarbonate
to free C02 or in terms of bicarbonate and P. See section on
blood. Direct experimental data for which equation (75) ex-
presses the fundamental relations are given as follows by Auer-
bach and Pick (1912):

pH values for mixtures of sodium carbonate and bicarbonate at 18 C. after
Auerbach and Pick

MOLS PES LITRE

MOLS PER LITHE

' NaHCOa

NasCOi

NaHCOs

Na2C03

0.20

0.00

8.35

0.10

0.000

8.35

0.19

0.01

8.90

0.09

0.005

8.98

0.18

0.02

9.15

0.08

0.010

9.30

0.16

0.04

9.45

0.07

0.015

9.50

0.14

0.06 •

9.65

0.06

0.020

9.60

0.12

0.08

9.96

0.05

0.025

9.87

0.10

10.10

0.04

0.030

10.05

0.08

0.12

10.35

0.03

0.035

10.23

0.06

0.14

10.45

0.02

0.040

10.35

0.04

0.16

10.65

0.01

0.045

10.7

0.02

0.18

11.0-11.8

0.00

0.050

11.4

0.00

0.20

11.59

324 THE DETERMINATION OF HYDROGEN IONS

Equation (76) is of importance when it is desired to know
the relations between- partial pressure of C02 and the state of
some carbonate equilibrium such as that of calcium carbonate.
In this case we have another set of relations. Calcium carbonate
is but slightly soluble per se. In the equilibrium equation

[Ca++] [CO,] = K
[CaC03]

we often have to deal with a constant value of CaC03 maintained
by the presence of solid CaC03. Under such circumstances we
may combine this constant with the dissociation constant giving

[Ca++] [C03] = K8 (78)

where K8 is the "solubility product."

By combining (78) with (76) it is seen how Ca++ can be gov-
erned by P, a relation of geological importance.

K8 varies with the nature of the solid phase, (Calcite, Aragonite
or precipitated calcium carbonate of different states of fineness).
It is of the order of 1 X 10-s.

The equations of carbonate equilibria have been left in their
more general form to show the more general relations. Modi-
fications for special purposes are very numerous and beyond
the scope of this sketch. For detailed treatment see references
under "Analyses," "Blood," "Water," "Equilibria," etc. A
treatment of the general biological importance of the carbonate
equilibria is given in The Fitness of the Environment by Henderson.

References. Auerbach-Pick (1912), Bjerrum-Gjaldbaek (1919),
Frary-Nietz (1915), Henderson (1913), Henderson-Black (1908),
Johnston (1915, 1916), Johnston-Williamson (1916), McClendon
(1917), McClendon-Shedlov-Thomson (1917), Michaelis-Rona
(1914), Prideaux (1915), Seyler-Lloyd (1917), Thiel-Stroheker
(1914), Tillmans (1921), Van Slyke (1917, 1922), Wagner-Enslow
(1922), Walker-Cormack (1900), Wilke (1921)-, Windish-Dietrich
(1920).

Catalysis. The catalytic activity of the hydrogen and the
hydroxyl ions in such transformations as the hydrolysis of cane
sugar has taken a prominent place in the development of the theory
of electrolytic dissociation. Under limited conditions one or an-

APPLICATIONS 325

other of these catalytic processes is proportional to the concentra-
tion of the hydrogen or the hydroxyl ions; but there may enter
the action of neutral salts. The theory of their influence is now
being recast in accord with the concept of "activity." The older
literature on hydrogen and hydroxyl ion catalyses is reviewed
in the monograph by Woker (1910, 1915). A few recent refer-
ences are: Abel (1920), Akerlof (1921), Jones-Lewis (1920), Kailan
(1920), Karlson (1921), Northrop (1921). See Enzymes, Salt
Action and Chapter XX.

Cerebrospinal Fluid.

References. Bisgaard (1913), Botazzi-Craifaleanu (1916), Col-
lip (1920), Felton-Hussey-Bayne-Jones (1917), Hertel (1921),
Hurwitz-Tranter (1916), Levinson (1917, 1919), Meier (1921),
Shearer-Parsons (1921), Weston (1916).

Cheese.

References. AUemann (1912), Barthel-Sandberg (1919), Okuda-
Zoller (1921), van Dam (1910).

Colloids. That the dispersion of colloids may be influenced
by the "reaction" of the medium has long been known. So widely
scattered is the literature on this particular phase of colloid chem-
istry that the author has made no attempt to assemble it. It
is through the study of protein solutions that the most distinctive
advances have been made. Beginning with Hardy the study
of proteins as amphoteric electrolytes has been carried forward
by Pauli, Michaelis, Robertson, S0rensen, Henderson, Loeb and
others until there has developed a distinct protest against the
separation of certain of the phenomena of colloids from the appli-
cation of the simpler relations of crystalloids. How far the matter
nay be pushed in its application to other types of material taking
he "colloidal state" remains to be determined.

A very good discussion of the relation of the developments in
>rotein chemistry to colloid chemistry is given by S0rensen (1917).
Compare Loeb, 1922.)

References. Abderhalden-Fodor (1920), Adolf -Pauli (1921),
Arrhenius (1922), Bethe (1920), Clowes (1913), Ellis (1911)
:,abes (1921), Lachs-Michaelis (1911), Lillie (1909), McBain-
! almon (1920), McDougal-Spoehr (1919), McGuire-Falk (1922),
: leier-Kronig (1921), Michaelis (1920, 1921, 1922), Michaelis-
:tona (1919-1920), Ostwald (1912), Perrin (1904), Procter (1921),

326 THE DETERMINATION OF HYDROGEN IONS

Rona-Michaelis (1919), Schoucroum (1920), Smith (1920),
Spiro (1916), Stiegler (1921), Varga (1919), Walpole (1914) /Will-
iams (1920). See also "Proteins," "Adsorption," "Donnan
Equilibrium," " Electrophoresis."

Comparative and General Physiology.

References. Aggazzotti (1913), Andrus (1919), Arrhenius (1921),
Atkins (1922), Barkan-Broemser-Hahn (1922), Barratt (1905),
Bernstein (1913), Bethe (1909), Brenner (1921), Broderick (1921),
Burgh-Clark (1921), Burridge (1920, 21), Carr (1921), Clowes-
Smith (1922), Cohn (1917), CoUett (1919, 1921), Collip (1920-
1921), Coulter (1920), Cremer (1906), Crozier (1915-19), Dale
(1913), Dale-Thacker (1914), Fletcher-Hopkins (1907), Galeotti
(1906, 1920), Garrey (1920), Girard (1909), Goldberger (1917)/
Gray (1920), Hampshire (1921), E. N. Harvey (1920), R. B.
Harvey (1920), Hastings-Murray (1921), Herbst (1904), Hirsch
(1921), Hiruma (1917), Hober (1910), Hopkins (1921), Hurwitz
(1910), Ivy-Oyama (1921), Jacobs (1920-22), Jameson-Atkins
(1921), Jewell (1920), Kahlenberg (1900), Kastle (1898), Kopac-
zewski (1914), Kfizencky (1916), Langefeldt (1921), J. Loeb,
(1898, 1903, 1904, 1906), Loeb-Wasteneys (1911), R. Loeb (1920),
Lloyd (1916), MacArthur (1920), McClendon (1916, 1920),
McClendon-Mitchell (1912), MacDougall (1921), Meyerhof (1918),
Mines (1912), Moore (1919, 1920), Moore-Roaf- Whitley
(1905), Moore-Whitley-Webster (1921), Morse-Goldberg
(1922), Neilson-Meyer (1921), Neugarten (1919), Oden (1916),
Ostwald-Kuhn (1921), Parnas-Wagner (1914), Pechstein
(1915), Philippson-Hannevart (1920), Plotho (1920), Popielski
(1919), Porcelli-Titone (1914), Powers (1921-22), Prentice-
Lund-Harbo (1920), Reichel (1922), Resch (1917), Richards
(1898), Ritchie (1922), Roaf (1912-1922), Rohde (1920), Rona-
Wilenko (1914), Roncati-Quagliariello (1921), Roth (1917),
Saunders (1920), Schwyzer (1914), Shelford-Powers (1915),
Shohl (1914), Straub-Meier (1919), Traube (1920), Warburg
(1910), Wells (1915), Whitley (1905), Wolf (1921).

Crystallography. Wherry (private communication) states
that there is reason to believe that the pH of a medium may some-
times control crystal form.

Culture of organisms other than bacteria, plants and tissue.

References. Bodine, (1921), Young-VanSant (1922). See also

APPLICATIONS 327

numerous notes in references under "Comparative and General
Physiology," "Bacteriology," and "Tissue culture."

Dakin's Solution.

Reference. Cullen- Austin (1918).

Digestive System. The digestive tract is primarily the chan-
nel for the intense activity of hydrolytic enzymes and as such is
provided with mechanisms for the establishment of hydrogen ion
concentrations favorable to these enzymes. Hydrogen electrode
methods have correlated the regional activity of particular en-
zymes with the reactions there found, have clarified some of the
differences between the digestive processes of infancy and adult
life, aided in the explanation of the acid and alkali formation, and
have been of service in the improvement of clinical methods for the
assay of pepsin activity and the diagnosis of abnormal secretion
of hydrochloric acid in the stomach. The control of specific phys-
iological functions such as secretion of conditioning agents (see
Bayliss, 1918), permeabilities, and activities of the varied muscu-
lature, as well as investigations upon the condition in the digestive
tract of substances such as calcium and phosphate which form in-
soluble precipitates are subjects which present promising material
for the application of modern methods. Shohl and King (1920)
have recently reviewed and improved methods of studying 'gas-
tric acidity.

References. Allaria (1908), Ambard-Foa (1905), Auerbach-
Pick (1912, 1913), Cannon (1907), Christiansen (1911, 1912,
1921), Davidsohn (1911, 1912, 1913, 1921), Foa (1905, 1906), Fow-
ler-Bergeim-Hawk (1915), Fraenckee (1905), Graham (1911),
Hahn (1914), Hainiss (1921), Hammett (1922), Hess (1915),
Hess-Scheer (1921), Howe-Hawk (1912), Huenekens (1914),
Krummacher (1914), Lanz (1921), Long-Fenger (1917),McClendon
(1915, 1920), McClendon-Bissell-Lowe-Meyer (1920), McClen-
don Myers-Culligan-Gydesen (1919), McClendon-Shedlov-Thom-
son (1917), McClendon-Shedlov-Karpman (1918), McWhorter
(1918), Menten (1915), Michaelis (1917, 1918, 1920), Michaelis-
Davidsohn (1910), Myers-McClendon (1920), Nelson-Williams
(1916), Okada-Arai (1922), Popielski (1919), Rolph (1915),
Rona-Neukirch (1912), Salge (1912), Scheer (1921), Schryver-
3inger (1913), Shohl (1920), Shohl-King (1920), Tangl (1906),
IYaube (1920), Ylppo (1916).

328

THE DETERMINATION OF HYDROGEN IONS

Dissociation Constants as determined with the hydrogen
electrode or indicator methods. Compare Chapter I.

References. Agostino-Quagliariello (1912), Dernby (1916),
Eckweiler-Noyes-Falk (1920), Eijdman (1906), Kastle (1905),
Kolthoff (1918, 1920), Michaelis (1911, 1913, 1914), Michaelis-
Garbendia (1914), Michaelis-Rona (1913, 1914, Prideaux (1911),
Salm (1906, 1908), Scudder (1914), Tizard (1910), Weisse-Meyer
Levy (1916). See Indicator constants.

Donnan Equilibrium. Imagine a solution of a simple elec-
trolyte and a membrane permeable to the electrolyte. Upon
one side of the membrane let there be a solution of a substance
which cannot penetrate the membrane but which can enter into
the equilibrium of the simple electrolyte. A simple case is the
following. Let the initial state be illustrated by the following
scheme where there is placed upon one side of the membrane
M a dilute solution of HC1 and upon the other side the acid HR
neither the anion nor the undissociated residue of which can
penetrate the membrane.

[HR],

[HC1]2

[H+]2

[CI].

Chlorine ions (or HC1) will diffuse from right to left until,
when equilibrium is attained, there will be the following state

[HC1]3

[HR],

[H+]3

[R]3

[CI].

[HC1],

[H+]4

[CI],

If now we place hydrogen electrodes on the two sides of the
membrane the E. M. F. of this gas chain will be determined in
part by the relative concentrations of the hydrogen ions and in
part by a potential difference across the membrane. This mem-
brane potential difference we shall call Ed

E.M.F. = 5Tln|5!I3
nF [H+]4

+ Ed

We may also place on the two sides electrodes, the potential
differences at which are determined by the relative concentrations

APPLICATIONS 329

of the chlorine ions (e. g. Pt-Cl electrodes or calomel electrodes).
For such a chain we would have

E.M.F. = — ln[2|4 + Ed
nF [Cl]3

We have already specified however that the system is at equilib-
rium. Therefore no energy could be obtained from either one
of the chains described above. The E. M. F. in each case is
then zero and since Ed is the same in each case

[H+]» = [Oj*

[H+]4 [a].

The rule of electrical neutrality indicates that on the right side
of the membrane [H+]4 = [Cl_]4. Combining this relation with
the other we then have

[H+]42 = [H+]3 [Cl]3

There are various directions in which we may now proceed.
As one example let us assume the very simple case where the
dissociations of HR and HC1 are complete, and let us further
assume that the system is divided by the membrane into two
equal parts. Between the initial and the final state of the sys-
tem chlorine ions have diffused from right to left until the con-
centration [Cl]3 is x. Then [H+]3 = [H+]x + x and [H+]4= [H+]s
— x. Introducing these values into the foregoing equation we
have

([H+]2 - x)2 = x ([H+], + x)

[H+]2 - x _ [H+]2 + [H+]i or x = [H+tf

x [H+]2 [H+li + 2[H+]2

The following table will give an idea of the magnitude of the
effects due to the conditions assumed.

As we have already indicated, the difference of potential be-

ween two hydrogen electrodes placed on opposite sides of the

) aembrane must, at the equilibrium state of the system, be equal

; nd opposite to the potential difference at the membrane. Hence

330

THE DETERMINATION OF HYDROGEN IONS

the membrane potential difference may be expressed in terms of
a hydrogen electrode gas chain:

RTln[H+]3
F [H+]/

By using this relation we calculate the membrane potential
difference given in millivolts in the last column of the following
table.

[Ri»-[H+],

[H+],

INITIAL KATIO

[H+J.

[H+],

PER CENT HC1
DIFFUSED TO

ESTABLISH
EQUILIBRIUM

EQUILIBRIUM
DISTRIBUTION

[H+],

RATIO z xr

[H+]4

MEMBRANE

POTENTIAL IN

MILLIVOLTS

0.01

1.0

1.0
1.0
0.01

0.01
1.0
100.0

49.8
33.3
0.98

1.01
2.0
101.0

- 0.3

- 18.0
-120.0

Of course the conditions assumed for purposes of illustration
are extremely simple but they suffice to indicate the nature of
relations of very great importance in the physiology of the living
cell.

References. Donnan (1911), Donnan-Harris (1911), Loeb
(1921-22), Michaelis (1922), Moore-Roaf-Webster (1912),
S0rensen (1917). See also "Blood," "Comparative and General
Physiology."

Dry-Cells.

Reference. Haller-Ritchie (1920).

Electroplating. The potential at which hydrogen is de-
posited freely upon an electrode is a function of the hydrogen ion
concentration of the solution. Therefore pH is important in
controlling gassy deposits. In addition it is found that buffer
solutions, maintaining the pH within definite limits, aid in the
production of desirable qualities in nickel deposits.

References. Bennett-Rose-Tinkler (1915), Blum (1920, 1921),
Kiister (1900), Thompson (1922).

Electrophoresis (Cataphoresis) and Electro-Osmosis.
An electrically charged body placed between an anode and a
cathode will tend to move toward the pole having a charge opposite
in sign to the charge on the body. If the body is a simple ion,
the movement is called ionic migration. If the body is a particle

APPLICATIONS 331

suspended in a medium such as water, the movement is called
electrophoresis. More generally it is known as cataphoresis.
The distinction between ionic migration and electrophoresis is
not always clear in the case of material in the colloidal state.

We shall not discuss the various theories advanced to account
for the experimental facts but shall treat briefly only that point
of view which it will be profitable to investigate further with
the aid of methods for determining pH.

Since acidic or basic ionization may determine the sign of the
charge upon a body of amphoteric nature the sign may be a func-
tion of the pH of the medium (aqueous). The direction of elec-
trophoresis is then a function of pH. At the isoelectric point
electrophoresis is a minimum. The position of this minimum on
the pH scale is a function of the acidic and basic dissociation con-
stants and the zone of the minimum may be narrow or broad
according to the relative magnitudes of the constants. See
Chapter 1. The method of electrophoresis is useful in determin-
ing isoelectric points.

There can be no movement such as that noted above without
a reciprocal interaction between suspended or dissolved material
and the dispersing medium. If then the charged particles are
fixed in position, as in the form of a porous diaphragm, are placed
in water and the whole subjected to a potential gradient, the
water will tend to move (electro-osmosis). The same relative
relations indicated above then hold. If the diaphragm is of an
amphoteric nature the direction of water flow will depend upon
the acidic and basic properties of the diaphragm and upon the
pH of the aqueous phase.

In either one of the two cases (particles fixed or free to move)
the same end result will be obtained if the particles adsorb hydro-
gen and hydroxyl ions according to such adsorption isotherma
that equality of adsorption and consequently equality of elec-
trical charge is attained at a definite pH value. On either side of
this pH value the excess adsorption of one or the other ion will
depend upon their concentrations which are a function of pH
by reason of the relation [H+] [OH-] = Kw. The position of this
"isoelectric" point is a function of the properties of the material
and may lie anywhere along the pH scale (according to the nature
of the material) with a narrow or broad isoelectric zone.

332 THE DETERMINATION OF HYDROGEN IONS

The converse to the above propositions is that nitration pro-
duces a potential difference across the filter which is a function
of the acidic and basic nature of the filter and of the pH of the
solution filtered.

Obviously the above sketch covers restricted conditions.

References. Barratt-Harris (1912), Briggs (1918), Freundlich
(1921) Gyemant (1921), Michaelis (1914, 1922), Perrin (1904-
1905), Porter (1921), Putter (1921), Steigmann (1920), Szent-
Gyorgyi (1920, 1921), Svedberg (1916), Svedberg-Anderson
(1919). See also "Isoelectric Point."

Enzymes. The activity of enzymes as influenced by the hy-
drogen ion concentration of the solution has occupied the atten-
tion of many investigators since the publication of S0rensen's
paper (1909). The analogy between the activity curves of several
enzymes and the curves relating the "dissociation residues" of
amphoteric electrolytes to pH suggested to Michaelis the ampho-
teric nature of enzymes (cf. Loeb 1909). Northrop has shown
important relations of activity to the acid-base nature of the
substrate. Holderer's observations on the extraction of enzymes
from cells with solvents of different reaction are most suggestive.
The necessity of controlling the pH of enzyme solutions for assays
as well as in the study of the effect of salts and in experiments
having to do with the formulation of the laws of enzyme activity
(Van Slyke and Cullen) is now generally recognized. Barendrecht
in the development of his radiation theory notes the special im-
portance of the hydrogen ions.

The following is a rough classification of studies on specific
enzymes.

Amygdalase. Bertrand-Compton (1921).

Amylase. Ambard (1921), Biederman-Rueha (1921), Euler-
Svanberg (1921), Falk-McGuire-Blount (1919), Maestrini (1921),
Groll (1920), McGuire-Falk (1920), Sherman (1919), Sherman-
Thomas-Baldwin (1919), Sherman-Schlessinger (1915), Sherman-
Thomas (1915), Sherman-Walker (1917), Sjoberg (1920),
Takamine-Oshima (1920).

Bacterial enzymes. Abderhalden-Fodor (1921), Avery-Cullen
(1920), Barthel-Sandberg (1920), Blanc-Pozerski (1920), Clark
(1920), Dernby (1917), Dernby-Blanc (1921), Groer (1912), Itano
(1916), Kanitz (1903), Lord (1919), Meyer (1911), Nye (1922),
Waksman(1918), West-Stevens (1921).

APPLICATIONS 333

Carboxylase. Neuberg (1915).

Catalase. Bodansky (1919), Burge (1920), Euler-Blix (1919),
Falk-McGuire-Blount (1919), Harvey (1920), Michaelis-Pechstein
(1913, 1914), Morgulis (1921), Phragmen (1919), Senter (1905),
S0rensen (1909), Sjoberg (1920), Waentig-Steche (1911).

Gellase. Bertrand-Holderer (1910).

"Diastases" (Important historical references) Fernbach (1906),
Fernbach-Hubert (1900).

Filtration of. Holderer.

Glycogenase. Norris (1913).

Coferments. Biederman (1921), Tholin (1921).

Emulsin. Bayliss (1912), Nordefeldt (1921), Vulquin (1910).
Willstatter-Csanyi (1921).

Erepsin. Euler (1907), Dernby (1916), Rona-Arnheim (1913).

Esterases (lipase). Avery-Cullen (1920), Baur (1909), David-
sohn (1912-1913), Falk, I. (1918), Falk, K. (1916), Groll (1920),
Haley-Lyman (1921), Hulton-Frankel (1917), Kastle (1902),
Rona (1911), Rona-Bien (1914), Rona-Reinicke (1921), Rona-
Michaelis(1911).

Invertase. Bertrand-Rosenblatt-Rosenblatt (1912), Euler
(1921), Euler-Laurin (1919, 1920), Euler-Svanberg (1918-21),
Fales-Nelson (1915), Falk-McGuire (1921), Fodor (1921), Griffin-
Nelson (1916), Hudson (1910), Hudson-Paine (1910), Kanitz
(1911), Langefeldt (1921), Michaelis (1921), Michaelis-Davidsohn
(1911), Michaelis-Menten (1913), Michaelis-Pechstein (1914),
Michaelis-Rothstein (1920), Nelson-Griffin (1916), Nelson-Hitch-
cock (1921), Nelson-Vosburgh (1917), Rona-Bach (1921), Rona-
Bloch (1921), Sjoberg (1921), S0rensen (1909), Vosburgh (1921).

Lactase. Davidsohn (1913).

Levanase. Kopeloff-Kopeloff-Welcome (1920).

Maltase. Adler (1916), Kopaczewski (1912, 1914, 1915),
Michaelis-Rona (1913, 1914), Rona-Michaelis (1913).

Oxidases, etc. Bunzel (1915), Bunzell (1916, 1917), Ohlsson
(1921), Menten (1919, 1920), Reed (1916), Rose-Kraybill-Rose
(1920).

Oxynitrilase. Krieble-Wieland (1921).

Pectase. Euler-Svanberg (1919).

Optimum temperature. Compton (1915, 1921). Euler-Laurin
(1920). • '

334 THE DETERMINATION OF HYDROGEN IONS

Papain. Frankel (1917). Chesnut (1920).

Peroxidase. Bouma-Van Dam (1918).

Pepsin. Christiansen (1912), Van Dam (1915), Davidsohn
(1912), Funk-Niemann (1910), Gies (1902), Graber (1921),
Groll (1920), Gyemant (1920), Loeb (1909), Michaelis (1918),
Michaelis-Mendelsohn (1914), Michaelis-Rothstein (1920), North-
rop (1919, 1920, 1921), Okada (1916), Pekelharing-Ringer
(1911), Ringer (1918), Rohonyi (1912), S0rensen (1909).

Phosphatase. Adler (1915).

Rennet. Allemann (1912), Van Dam (1908, 1909, 1912, 1915),
Funk-Niemann (1910), Madsen-Walbum (1906), Michaelis-
Mendelsohn (1913), Michaelis-Rothstein (1920), Milroy (1915),
Thaysen (1915).

Salivary diastase (ptyalin). Cole (1903), Hahn-Harpuder
(1920) Michaelis-Pechstein (1914), Ringer-Trigt (1912). See
amylase.

Taka-diastase. Okada (1916).

Trypsin. Auerbach-Pick (1913), Hahn-Mickalik (1921), Ka-
nitz (1902), Michaelis-Davidsohn (1911), Northrop (1921, 1922),
Palitzsch-Walbum (1912). Ringer (1921), Robertson-Schmidt
(1908).

Theory of action. Barendrecht (1920), Euler (1920), Falk
(1921), Loeb (1909), Michaelis (1909. 1914), Michaelis-Davidsohn
Mad 1911), Rohonyi (1911), Van Slyke-Cullen (1914).

Urease. Barendrecht (1920), Lovgren (1921), Onodera (1915),
Rona-Gyorgy (1920), Rona-Petrov (1920), Van Slyke-Cullen
(1914), Van Slyke-Zacharias (1914).

Equilibria. The hydrogen electrode and indicators in the
determination of affinity constants, free energy, hydrolysis, etc.

References. Adolf-Pauli (1921), Bjerrum (1907-21),
Boeseken-Kerstjens (1916), Bogue (1920), Chow (1920),
Denham (1908), Eucken (1907), Ellis (1916), Ferguson' (1916),
Frary-Nietz (1915), Fricke (1920), Hardman-Lapworth (1911),
Harned (1915-1922), Heyrovsky (1920), Jahn (1900, 1901),
Kanitz (1921), Lewis (1908, 1912, 1913), Lewis-Brighton-Se-
bastian (1917), Lewis-Randall (1914), Linhart (1919), Loffler-
Spiro (1919), Loomis-Acree (1911), Loomis-Essex-Meacham
(1917), Lowenherz (1896), Margaillan (1913), McBain-Coleman
(1914), Maclnnes (1919), Merrill (1921), Nernst (1889), Newbery

APPLICATIONS 335

(1914), Noyes-Ellis (1917), Noyes-Freed (1920), Richards-Dun-
ham (1922), Rosenheim-Leyser (1921), Tizard (1910), Tizard-
Boeree (1920), Tolman-Greathouse (1912). See also Chapters
IV, VI, XVI.

Explosives.

References. Farmer (1920), Angeli-Errani (1920).

Feces. See "Digestive System."

Filtration. Hydrogen ion concentration, through its influ-
ence upon the dispersion of certain colloids and upon the condi-
tioning of filter material, may control the filterability of a sub-
stance. Holderer's thesis from Perrin's laboratory presents in
admirable form many of the theoretical aspects of the subject. A
republication of this rare thesis is desired. The subject is not only
of considerable theoretical interest but also of great practical
importance. Buffer control with indicator tests' may in many in-
stances facilitate filtrations upon an industrial as well as a labo-
ratory scale.

References. Aubel-Colin (1915), Holderer (1909, 1910, 1911,
1912), Homer (1917), Loeb (1919), Schmidt (1914), Strada (1908),
Wilson (1921), Wilson-Copeland-Heisig (1921), Wilson-Heisig
(1921). See also "Electrophoresis."

Foods, pH of. The National Canners' Laboratory has made
a number of determinations of the pH of canned foods. See
"Canning." See also "Milk," "Cheese," "Wine," "Beer," "Vine-
gar," references given by Clark and Lubs (1917)1 and the paper
by McClendon and Sharp (1919). The influence of the pH upon
the stability of a "vitamine" has been studied by La Mer (1921),
and Campbell, LaMer and Sherman (1922). cf. Harden and
Zilva (1918). For sterilization of canned goods see "Disinfec-
tion" under "Bacteriology" and "Canning".

Glass, effect of, on reaction of solutions.

References. Esty-Cathcart (1921), Ewe (1920), Fabian-Stull
(1921), Levy-Cullen (1920), Russell-Nichols-Stimmel (1920).

Glucose, decomposition of, as influenced by pH.

References. Elias-Kolb (1913), Euler-Hedelius (1920), Hen-
derson (1911), Mathews-McGuigan (1907), Michaelis-Rona

1 Some of the pH values given by Clark and Lubs for acidified or alka-
linized extracts have been misquoted as the pH values of the original
material.

336 THE DETERMINATION OF HYDROGEN IONS

(1909-1912), Nef (1913), Rona-Arnheim (1913), Rona-Doblin
(1911), Rona-Wilenko (1914). Also references in Woker.

Hemolysis ,

References. Atkin (1911, 1914), Cook-Mix-Culvyhouse (1921),
Coulter (1921), Fenn, (1922), Fuhner-Neubaur (1907), Gros
(1910), Haffner (1920), Hellens (1913), Jodlbauer-Haffner (1920,
1921), Jordan (1903), Kozawa (1914), Krogh (1909), Lagrange
(1914), Michaelis-Skwirsky (1909), Michaelis-Takahashi (1910),
Stevens-Koser (1920), Teague-Buxton (1907), Walbum (1914,
1915).

Hydrolysis. The reaction between an acid and a base is
reversible.

HA + BOH ?=± BA + H20

♦

There are present then both free acid and free base even when
the two are mixed in equivalent proportions. This last condition
can be duplicated by making up the solution in the first place
with the pure salt. The above reaction then goes from right to
left until the equilibrium state is reached and the process is
called hydrolysis, because it may be regarded as a splitting
of water molecules.

Now the resulting acid and base ionize, the one tending to
increase the hydrogen ion concentration, the other tending to
increase the hydroxyl ion concentration. If the acid is more
highly dissociated than the base the solution will contain more
hydrogen ions than hydroxyl ions; and if the base is more highly
dissociated than the acid the solution will contain more hydroxyl
than hydrogen ions. Since the magnitude of a dissociation con-
stant is a measure of dissociation tendency the reaction of a salt
solution will depend upon the relative magnitudes of the Ka
and Kb constants of the component acid and base.

In a solution of the salt, BA, we have present BA, B+, A-,
HA, BOH, H+ and OH.~

By the rule of electrical neutrality [A~] + [OH"] = [B+] +
[H+]. Since total acid = total base, [HA] + [A~] + [BA] = [B+]
-f [BOH] + [BA]. Introducing the acid and the base equilib-
rium equations and the relation [H+] [OH-] = Kw and combining
these equations we have

mn = VK- '

Kb (K. + [Ai)

APPLICATIONS 337

If now Kb and Ka are small in relation to [B+] and [A-], and
if the solution is sufficiently dilute so that [B+] and [A-] each
approximate the salt concentration [S], then approximately

[h+] = VKwi^

Cf. formula for isoelectric point of ampholyte. When Ka = Kb,
[H+] = 10-7, pH = 7.

If we are dealing with a salt, the acid component of which
is very "strong" we may regard the acid set free by the hydroly-
sis of the salt as completely dissociated. [HA] in the above equa-
tions is placed equal to zero and we then derive

[H+]= ^(Kh + [B+])
" Kb

If now Kb is small in relation to [B+] and if [B+] approxi-
mates [S]

[H+] approximates \— - [S]
™ Kb

Conversely when the base is very strong and when the same
assumptions made above are maintained

[H+] approximates W

KaKv

[S]

References. See treatment by Bjerrum (1914), example by
Denham (1908), and numerous references under "Equilibria."

Indicator Constants. See Prideaux and Chapters IV and
VIII.

, References. Clark-Lubs (1917), Gillespie (1920), Paulus-Hut-
chinson-Jones (1915), Kolthoff (1918-1922), Michaelis (1920),
Michaelis-Gyemant (1920), Michaelis-Kriiger (1921), Rosenstein
(1912), Schaeffer-Paulus-Jones (1915), Salm (1904), Tizard (1910).

Indicators, natural.

References. Bribaker (1914), Crozier (1916, 1918), Haas (1916),
Pozzi-Escot (1913), Sacher (1910), Scheitz (1910), Stephanides
(1916), Trillat (1916), Walbum (1913), Watson (1913). See also
Perkin and Everest.

338 THE DETERMINATION OF HYDROGEN IONS

Industrial Processes. See every subject in this chapter.
Also the following special references.

References. Brewster-Raines (1921), Clark-Zoller-Dahlberg-
Weimar (1920), Keeler (1922), Lubs (1920), Searle (1920), Wil-
son-Copeland-Heisig (1921), Wilson-Heisig (1921), Zoller/1921),
and references on "Water Works" and "Leather."

Isoelectric Points. See Chapter I.

References. Brossa (1915), Cohn (1920-1922), Cohn-Gross-
Johnson (1920), Eckweiler-Noyes-Falk (1920), Fodor (1920),
Loeb (1918-1922), Michaelis (1911-1920), Michaelis-Bien (1914),
Michaelis-Davidsohn (1910-1913), Michaelis-Grineff (1912),
Michaelis-Mostynski (1910), Michaelis-Pechstein (1912), Michae-
lis-Rona (1919), Michaelis-Takahashi (1910), Mills (1921),
Rona-Michaelis (1910), S0rensen (1912, 1917), Stuber-Funck
(1921), Szent Gyorgyi (1921), Thomas-Kelley (1922).

Leather and Tanning.

References. Atkin (1922), Atkin-Atkin (1920), Atkin-Thomp-
son (1920), Balderston (1913), Procter (1921), Procter-Wilson
(1916), Povarnin (1915), Sand-Law (1911), Thomas-Baldwin
(1919), Thomas-Foster (1921), Thomas-Kelly (1921, 1922),
Wilson (1917, 1921), Wilson-Daub (1921), Wilson-Kern (1921),
Wood-Sand-Law (1911). See also "Proteins."

Milk.

References. Allemann (1912), Aron (1914), Baker-Breed (1920)/
Baker-Van Slyke (1919), Chapman (1908), Clark (1915), Clark-
Cohen (1922), Cooledge-Wyant (1920), van Dam (1908, 1918),
Davidsohn (1912, 1913), Foa (1905, 1906), Hastings-Davenport
(1920), Jones (1921), Kramer-Green (1921), Laqueur-Sackur
(1903), Milroy (1915), Palmer-Dahle (1922) Rogers-Deysher-
Evans (1921), Rona-Michaelis (1909), Schultz-Chandler (1921),
Schultz-Marx-Beaver (1921), Sommer-Hart (1919, 1920), Stut-
terheinn, Szili (1917), Taylor (1913), Terry (1919), Till-
mans-Obermeier (1920), Van Slyke-Baker (1918, 1919). See also
"Cheese" and "Protein."

Neuro-physiology.

References. Adrian (1920), Bottazzi-Craifaleanu (1916), Chid
(19,07), Garry (1920), Grant (1920), Mansfield-Szent Gyorgyi
(1920), Mayer (1916), Moore (1919), Neugarten (1919), Zotter-
man (1921). See also "Blood," (the respiration phase) and
"Comparative and General Physiology."

APPLICATIONS 339

Permeability of cells.

References. Bethe (1922), Clowes-Smith (1922), Collander
(1920), Donnan (1911), Haas (1916), Harvey (1911, 1913), Haynes
(1921), Holderer (1911), Jacob j (1920), Lillie (1909), Moore-Roaf-
Webster (1912), Oden (1916), Reemelin-Isaacs (1916), Snapper
(1913), Stiles-Jorgensen (1915), compare Filtration.

Phagocytosis.

References. A. Evans (1921, 1922), Hamberger-Heckma (1908) ,
Koltzoff (1914), Radsma (1920), Sawtchenko-Aristovsky (1912),
Schwyzer (1914).

Pharmacology, etc. pH in relation to properties, activity,
deterioration, and assay or detection of drugs.

References. Adams (1917), Crane (1921), Evers(1921),v.Groer-
Matula (1920), Hanzlik (1920, 1921), Kolthoff, (1920, 1922),
Leech (1922), Levy-Cullen (1920), Macht-Shohl (1920), Meier-
Kronig (1921), Mellon-Slagle-Acree (1922), Menten (1920),
Moore (1920), Rippel (1920), Rona-Bach (1920), Shohl-Deming
(1921), Snyder-Campbell (1920), Sollmann (1917), Tsakalotos-
Horsch (i914), Williams-Swett (1922), Zoccola (1918).

Phyto-pathology and Physiology.

References. Atkins (1922), Chambers (1921), Clevenger (1919),
Crozier (1919), Harvey (1920), Hixon (1920), Lapicque (1921),
MacDougal (1921), Martin (1921), Schmitz (1919), Schmitz-
Zeller (1919), Webb (1919), Wherry (1918-22), Wolf-Foster
(1921), Wolf-Shunk (1921), Zeller-Schmitz (1919).

See "Plant Distribution," "Comparative and General Physi-
ology," "Soil."

Plant Distribution. Wherry, working with a simple field
kit, has carried indicators into the field and has correlated the
habitats of several plant species with the pH of their soils.

Investigations by O. Arrhenius in Sweden, by Olsen in Denmark
and by Atkins in England and India have confirmed Wherry's
observation that the pH of the soil is of great significance.

Such information has contributed toward methods of cultivat-
ing the blueberry and wild-flowers hitherto unknown or un-
common in garden and greenhouse.

References. Arrhenius (1920, 1922), Atkins (1921, 1922),
bomber (1921), Emerson (1921), Fisher (1921), Gail (1919),
)lsen (1921), Wherry (1920-1922). See also "Phytopathology
tnd Physiology," " Soils," "Water," and especially " Bacteriology."

34:0 THE DETERMINATION OF HYDROGEN IONS

Proteins, by reason of their chemical structure, are amphoteric.
As such they are subject to the pH of aqueous dispersing media
as are the simple ampholytes. Though complete equilibrium
equations are difficult to formulate we should expect the occur-
rence of pH points and zones comparable to the isoelectric points
and zones of simple ampholytes. Experimentally these have
been found. These are also points of optima, or minima, for
various properties of protein solutions (e.g. minimal electrophore-
sis, viscosity and osmosis). If the solubility of the protein itself
is less than that of its acid or basic salts, the protein can be pre-
cipitated at or near the isoelectric point (e.g. analysis and com-
mercial preparation of casein). Closely related is the adjustment
of pH favoring separation of crystals. Proteins are unable to
penetrate many membranes but are able to enter into an acid-
base equilibrium and thus exhibit many interesting relations in
Donnan equilibria (S0rensen, Loeb).

The outstanding difficulty in treating proteins as electrolytes
is the establishment of exact quantities for concentrations or
activities which must necessarily be used in formulating equilib-
rium equations. The mathematical treatment by Michaelis
and by S0rensen, and especially the painstaking experimental
investigations to which S0rensen and his coworkers have devoted
several years have advanced the subject beyond dependence on
mere analogy to the conduct of simple ampholytes.

References. Adolf -Spiegel (1920), Agostino-Quagliariello (1912),
Atkin (1920), Bogue (1921), Bovie (1920), Bugarszky-Liebermann
(1898), Burrows-Cohn (1918), Chiari (1911), Chick (1913),
Chick-Martin (1910-13), Clark-Zoller-Dahlberg-Weimar (1920),
Cohn (1920-22), Cohn-Gross-Johnson (1920),Davis-Oakes-Browne
(1921), Ferguson-France (1921), Field (1921), Fodor (1920-21),
Haas (1918), Handovsky (1910), Hardy (1899, 1905), Henderson-
Cohn-Cathcart-Wachman-Fenn (1919), Henderson-Palmer-Neu-
burgh (1914), Hill (1921), Hitchcock (1922), Laqueur-Sackur,
(1903), Lloyd (1920, 1922), Loeb (1918-22), Manabe-Matula
(1913), Michaelis (1909), Michaelis-Airila (1921), Michaelis-
Mostynski (1910), Michaelis-Rona (1910, 1919), Michaelis-
Szent Gyorgyi (1920), Mills (1921), Okuda-Zoller (1921), Oryng-
Pauli (1915), Palmer-Atchley-Loeb (1921, 1922), Patten-John-
son (1919), Patten-Kelems (1920), Pauli (1903-1922), Pauli-

APPLICATIONS 341

Handovsky (1908-10), Pauli-Matula (1919), Pauli-Samec (1909-
14), Pauli-Wagner (1910), Pechstein (1913), Procter-Wilson
(1916), Quagliariello (1912), Resch (1917), Robertson (1907-
1918), Rohonyi (1912), Ryd (1917, 1918), Sharp-Gortner (1922),
Schmidt (1916), Schorr (1911), Sollmann (1917), S0rensen (1917-
1921), S0rensen & coworkers (1917), S0rensen-Jiirgensen (1911),
Spiro (1904, 1913), Starke (1900), Szent-Gyorgyi (1920, 1921),
Thomas (1921), Wagner (1921), Wintgen-Kriiger (1921), Wint-
gen-Vogel (1922), Ylppo (1913), Zoller (1921). See also "Iso-
electric Point."

Salt-Action, theory and effects in relation to pH. See Chap-
ters I, II, and VII.

References. Abegg-Bose (1899), Arrhenius (1888, 1889), Aker-
lof (1921), Brightman-Meachem-Acree (1920), Chick-Martin
(1912, 1913), Falk (1918, 1920), Gillespie- Wise (1918), Harned
(1915), Haynes (1921), Hofmeister (1891), Holm-Sherman (1921-
1922), Kolthoff (1916-22), Lloyd (1916), Loeb (1906-1922),
McBain-Coleman (1914), McClendon-Mitchell (1912), Michaelis
(1914, 1920), Michaelis-Rona (1909), Michaelis-Szent Gyorgyi
(1920), Michaelis-Timenez Dias (1921), Northrop (1920), Poma
(1914), Poma-Patson (1914), Prideaux (1919), Rose-Kraybill-Rose
(1920), Rosenstein (1912), Ryd (1917), Shearer (1920), Sherman-
Thomas (1915), S0rensen-Palitzsch (1913), S0rensen-S0rensen-
Linderstr0m Lang (1921), Spiro (1921), Szent-Gyorgyi (1920),
Szyszkowski (1907), Thomas Baldwin (1919), Wells (1920), See
especially references in Chapter II on "Activity."

Serology. See also Acid Agglutination of Bacteria, Hemolysis,
Bacteriology, Proteins, Colloids.

References. Amako (1911), Atzler (1914), Brooks (1920),
Buchanan (1919), Coulter (1921), Enlows (1922), Evans (1921,
22), Field-Teague (1907), Hirsch-Peters (1922), Homer (1917,
1918, 1919), Landensteiner (1913), Landensteiner-Prasek (1913),
Langenstrass (1919), Lindenschatt (1913), Leschly (1916), Ma-
son (1922), Michaelis-Davidsohn (1912), Neukirch (1920), No-
guchi (1907), Ruppel (1920), Tulloch (1914, 1918).

Sewage.

References. Clark-Cohen (1922), Wilson-Copeland-Heisig
(1921), Wilson-Heisig (1921).

342 the determination of hydrogen ions

Soap Solutions.

References. Beedle-Bolam (1921), McBain (1920), McBain-
Bolam (1918), McBain-Martin (1918), McBain-Salmon (1920).

Soil Acidity has been confused by the complexities of titri-
metric procedures, has been neglected, or has been considered to be
an unreality by one or another school. Gillespie (1916) obtained
good agreement between pH values of soil extracts determined
by means of the hydrogen electrode and again by means of indi-
cators. The practical significance of this is now revealed by
studies which show characteristic pH values for well-defined types
of soil, which show correlations between the pH of soil extracts
and the growth of beneficial or harmful microorganisms, and
which show correlations between the natural distribution of
plants and the pH of the soils in which they are found.

References. Arrhenius (1921, 1922), Atkins (1922), Bjerrum-
Gjaldbaek (1919), Blair-Prince (1920), Carr (1921), Comber
(1920), Conner (1921), Crouther (1920), Demolon (1920), Dug-
gar (1920), Erdman (1921), Fisher (1914, 1921), Gainey (1918,
1922), Gillespie (1916-1918), Gillespie-Hurst (1918), Hibbard
(1921), Hoagland (1917-1918), Hoagland-Christie (1918), Hoag-
land-Sharp (1918), Hudig-Strum (1919), Joffe (1920), Jones-
Shive (1920), Kappen (1916), Kappen-Zapfe (1917), Kelley-
Cummins (1921),. Knight (1920), Kobayashi (1920), Lipman-
Joffe (1920), Lipman-Waksman-Joffe (1921), Loew (1903),
xMcCall-Haag (1920, 1921), MacDougal (1920), Martin (1920,
1921), Meier-Halstead (1921), Morse (1918, 1920), Oden (1916-
21), Olsen (1921), Plummer (1918), Rice-Osugi (1918), Robinson
(1921), Robinson-Bullis (1921), Saidel (1913), Salter-Mcllvaine
(1920), Schollenberger (1921), Sharp-Hoagland (1916, 1919),
Stephenson (1919, 1921), Stocklasa (1922) Swanson-Latshaw-
Tague (1921), Tijmstra (1917), Truog (1918), Truog-Meacham
(1919), Waksman (1922), Weis (1919), Wherry (1916-1922).
See also "Plant Distribution."

Solubility. The true solubility of a compound may be
regarded as independent of the hydrogen ion concentration of a
solution; but if the compound is an acid, base, ampholyte or salt
some of the material present in solution is ionized and this portion
is governed by the ionic equilibrium of which the hydrogen ion
concentration is a part. Therefore the total solubility which is

APPLICATIONS 343

generally of more importance than the true, partial solubility
is a function of pH.

[H+] [A-]
Consider the equilibrium — =77: — = Ka and assume that

LH-AJ

the solubility of the acid HA itself is low so that we shall not
encounter the difficulties inherent in the treatment of concen-
trated solutions. If the acid is present in the solid phase [HA]
is maintained constant and is the partial solubility, Sp. On
combining the constants in the above equation we have [H+]
[A-] = Ks where Ks is the solubility product. The total solu-
bility, St is then equal to the true partial solubility, Sp, plus [A-] or

*•_« , j^ q _* nH+] ± Kal

»t — &p -r rjj+i' or °t — &p ru+i

If there is present no salt of the acid to furnish [A-]

[Hi2 = K8
or

pH = - } log K8

For the case of calcium carbonate, the [C03 ] from which is
controlled by [H+], see "Carbonate Equilibria."

References. See any text on physical chemistry and "Carbon-
ate Equilibria," "Protein," "Equilibria," etc.

Staining.

References. Agulhon-Leobardy (1921), Bethe (1922), Jodl-
bauer-Haffner (1921), MacArthur (1921), Michaelis (1920),
Ponselle (1919), Rohde (1920).

Surface Tension.

References. Adam (1921), Bottazzi-Agostino, Ellis (1911),
Haber-Klemensiewicz (1909), Hartridge-Peters (1920), Micha-
elis (1909), Schwyzer (1914), Traube (1920), Williams (1920),
Willows-Hatschek (1919), Windish-Dietrich (1919-1922).

Sweat.

References. Clark-Lubs, (1917), Talbert (1919). •

Tautomerism other than of indicators.

References. Biddle-Watson (1917), Fraenkel (1907) Mur-
chauser (1920), Nelson-Beegle (1919).

Tissue Culture.

References. Felton (1921), Fischer (1921), Lewis-Felton (1921).

344 THE DETERMINATION OF HYDROGEN IONS

Urine and Kidney Functions. The excretion of acids and
bases in the urine is one of the mechanisms by which the hydrogen
ion concentration of the blood is preserved constant. For this
reason the determination of the acid-base equilibria in the urine
in their relation to the potential acid-base intake in the food and
the degree of oxidation of food material is of importance in
fundamental physiological researches and in clinical studies.
Besides references to be found under "Blood" the following are
some of the more special references on urine.2

References. Auerbach-Friedenthal (1903), Biehler (1920), Biltz-
Hermann (1921), Blatherwick (1914), Bugarszky (1897), Carr
(1921), Collip-Backus (1920), Cushny (book 1917), Fiske
(1920, 1921), Fitz-Van Slyke (1917), Foa (1905), Gamble (1922),
Guillaumin (1920), Hanzlik (1920), Haskins (1919), Hasselbalch
(1916), Henderson (1910, 1911, 1914), Henderson-Palmer (1913)
Henderson-Spiro (1908), Hober (1902), Hober-Jankowsky (1903)
Hollo (1921) a Howe-Hawk (1914), Macleod-Knapp (1918)
Marshall (1922), Nagayama (1920), Nelson-Williams (1916)
Newburgh-Palmer-Henderson (1913), Palmer-Henderson (1915)
Palmer-Salvesen-Jackson (1920), Quagliariello-d'Agostino (1912)
Reemelin-Issacs (1916), Rhorer (1901), Ringer (1909, 1910)
Rohde (1920), Schemensky (1920), Schloss-Harrington (1919)
Shohl (1920), Skramlik (1911), Stillman-Van Slyke (1917), Tal-
bert (1920), Van Slyke-Palmer (1919, 1920).

Vinegar.

Reference. Clark-Lubs (1917), Brode-Lange (1909), Kling-
Lassieur-Lassieur (1922).

Water (sea and fresh). The carbonate equilibrium maintains
sea water at a very constant pH which has doubtless varied with
the C02 tension of the atmosphere in geological ages and which
varies somewhat with the temperature, and locally with accretions
from rivers and springs and contact with geologic deposits. The
wider aspects of the carbonate equilibria involved have been
described in Henderson's Fitness of the Environment. The chart-
ing of the pH values for different regions of the seas has been
of aid in oceanographic surveys and in some instances has been
of value in the study of plant and animal distribution. (See
"Plant Distribution" and "Comparative Physiology.")

* See Clark and Lubs (1917) for some examples 'of the application of the
sulfon phthalein indicators to the determination of the pH of urines.

APPLICATION'S 345

Fresh waters are influenced chiefly by the deposits with which
they come in contact. pH determinations in the field are of aid to
the geologist in demarking waters of limestone origin (Wherry
private communication) .

In the clarification of water by "alum" or "iron" coagulation
the pH of the final mix determines the percentage coagulant thrown
out, the time required for floe formation and the efficiency of
color- and turbidity-removal. There is also a probable relation
to the efficiency of the filtration process itself.

The hydrogen ion enters into every equilibrium of importance
to water softening and to corrosion.

References. Auerbach (1904), Baylis (1922), Buswell (1922),
Corti-Alvarez (1918), Crozier (1920), Gaarder (1916-1917),
Greenfield-Baker (1920), Haas (1916), Henderson (1913), Hen-
derson-Cohn (1916), Heyman (1920), Kolthoff (1921), Loeb
(1904), McClendon (1916, 1917), Mayer (1919), Massink (1920),
Massink-Heyman (1921), Michaelis (1914, 1921), Palitzsch
(1911, 1915, 1916), Powers (1921, 1922), Prideaux (1919), Ringer
(1908), Ruppin (1909), Saunders (1921), Shelf ord (1919), Smith
(1919), Snook (1915), S0rensen-Palitzsch (1910-13), Stephanides
(1916), Tillmans (1919, 1921), Trillat (1916), Wagner-Enslow
(1922), Walker-Kay (1912), Wells (1921), Wolman-Hannan (1921).

Water, pure. Ionization of.

References. Kohlrausch-Heydweiller (1894), Lewis, Brighton
and Sebastian (1917), Nernst (1894), Ostwald (1893), Wijs (1893).

Wine Acidity. Besides influencing the fermentations, the pH
of wine has been found to correlate in a general way with the acid
taste.

References. Casale (1919), Dutoit-Dubroux (1910), Paul
(1914, 1915, 1916), Quartaroli (1912).

BIBLIOGRAPHY

Knowledge is of two kinds . We know a subject ourselves, or we
know where we can find information upon it. — Samuel Johnson.

The references in this bibliography are classified either by notations
given at the end of each chapter or else by the subjects briefly outlined in
Chapter XXI where cross references have been reduced to a minimum.

Abbreviations follow for the most part the system adopted by Chemical
Abstracts.

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Studien uber den fermentativen Abbau von Polypeptiden.

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Abderhalden, E., and Fodor, A. 1920 Studien iiber die Adsorption

von Aminosauren, Polypeptiden und Eiweisskorpern durch

Tierkohle. Beziehungen zwischen Adsorbierbarkeit und gelo-

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Abderhalden, E., and Fodor, A. 1921 Der Einfluss von Zusatzen

(Toluol, Chloroform, Thymol und ferner von Neutralsalzen)

auf den fermentativen Abbau von Dipeptiden durch Hefeauszug.

Fermentforschung, 4, 191.
Abegg, R. 1902 Uber die Komplexbildung von Quecksilbersalzen. Z.

Elektrochem., 8, 688.
Abegg, R. 1904 Elektrodenvorgange und Potentialbildung bei mini-

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Abegg, R., Atterbach, F., and Luther, R. 1909 Zur Frage des Null-

punktes der elektrochemischen Potentiale. Z. Elektrochem.,

15, 63.
Abegg, R., Auerbach, F., and Luther, R. 1911 Messungen elektromo-

torischer Krafte galvanischer Ketten. Abhandl. d. Deutschen

Bunsen-Gesellschaft, No. 5. Halle, 1911.
Abegg, R., and Bose, E. 1899 Ueber den Einfluss gleichioniger Zusatze

auf die elektromotorische Kraft von Konzentrationsketten und

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Abel, E. 1920 Kinetik der Wasserstoffsuperoxyd-Jod-Reaktion. Z.

physik. Chem., 96, 1.
Abel, E., and Furth, O. v. 1906 Zur physikalischen Chemie des Oxy-
hemoglobins. Das Alkalibindungsvermogen des Blutfarb-

stoffes. Z. Elektrochem, 12, 349.
Acree, S. F. 1907 On the constitution of phenylurazole, III. Contribu-
tion to the study of tautomerism. Am. Chem. J., 38, 1.
Acree, S. F. 1908 On the theory of indicators and the reactions of phthal-

eins and their salts. Am. Chem. J., 39, 529.
346

BIBLIOGRAPHY 347

Acree, S. F., Mellon, R. R., Avert, P. M., and Slagle, E. A. 1921 A
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Acree, S. F., and Slagle, E. A. 1908 On the theory of indicators and the
reactions of phthaleins and their salts. Am. Chem. J., 39, 789;
1909, 42, 115.

Adam, A. 1921 Ueber das H-Ionenoptimum der Kopfchenbakterien des
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Adam, A. 1921 Ueber den Einfluss der H-lonenkonzentration des Nahr-
bodens auf die Entwicklung des Bacillus bifidus. Z. Kinder-
heilk., 29, 306.

Adam, A. 1922 Ueber die Bedeutung der Eigenwasserstoffzahl (des
H-Ionenoptimum) der Bakterien. Centr. Bakt. Parasitenk. 1.
Abt. (orig.),87,481.

Adams, E. Q., and Rosenstein, L. 1914 The color and ionization of
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Adam, N. K. 1921 The properties and molecular structure of thin films of
palmitic acid on water. Proc. Roy. Soc. (London), 99 A, 336.

Adams, H. S. 1917 The thermal decomposition of the oxytocic principle
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Adler, L. 1915 tJber die Phosphatasen im Malz. Biochem. Z., 70, 1.

Adler, L. 1915-16 Uber den Einfluss der Wasserstofflonen auf die Wirk-
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Adler, H. M., and Blake, G. 1911 The retention of alkali by the kidney
with special reference to acidosis. Arch. Internal Med., 7, 479.

Adolf, M., and Pauli, W. 1921 Die physikalisch-chemische Analyse
der Aluminiumoxysalze und Aluminiumoxydsole. Kolloid-Z.,
29,281.

Adolf, M., and Spiegel, E. 1920 Untersuchungen liber physikalische
Zustandsanderungen der Kolloide. XXIII. Das Acidalbumin.
Biochem, Z., 104, 175.

Adrian, E. D. 1920 The recovery process of excitable tissues. Part I.
J.Physiol., 54, 1.

Aggazzotti, A. 1907 Existe-t-il un rapport entre la reaction vraie et la
reaction potentielle du sang a la pression et dans l'air rarefied
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Aggazzotti, A. 1913 La reazione dei liquidi dell' ovo durante lo sviluppo.
Archiv. fur Entwicklungsmechanik 37, 1.

Aggazzotti, A. 1921 La secrezione salivare nella marcia in montagna.
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Agostino, E. D', and Quagliariello, G. 1912 SulF applicazione delle
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Agulhon, and Leobardy, J. de 1921 Remarques sur l'emploi en hema-
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348 THE DETERMINATION OF HYDROGEN IONS

Akerlof, G. 1921 Die Neutralsalzwirkung bei hoheren Salzkonzentra-
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Allaria, G.B. 1908 Untersuchungen iiber Wasserstoff-Ionen Konzen-
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Allen, E. R. 1919 Some conditions affecting the growth and activities

of Azotobacter chroococcum. Ann. Missouri Bot. Garden, 6, 1.
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Allemann, O. 1912 Die Bedeutung der Wasserstoffionen fur die Lab-

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Ambard, L. 1921 Amylase; its estimation and the mechanism of its

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Andrus, E. C. 1919 Alterations in the activity of the terrapin's heart
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Angeli, A., and Errani, G. F. 1920 Acidity in smokeless powders.

Gazz. chim. ital., 50, 139 (cited).
Anger, V. 1921 Sur l'emploi des indicateurs colores en acidim^trie

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Arrhenius, O. 1920 Ocologische Studien in den Stockholmer Scharen.

Stockholm.
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Arrhenius, O. 1922 Hydrogen ion concentration, soil properties and
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350 THE DETERMINATION OF HYDROGEN IONS

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352 THE DETERMINATION OP HYDROGEN IONS

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354 THE DETERMINATION OF HYDROGEN IONS

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356 THE DETERMINATION OF HYDROGEN IONS

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358 THE DETERMINATION OF HYDROGEN IONS

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360 THE DETERMINATION OF HYDROGEN IONS

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362 THE DETERMINATION OF HYDROGEN IONS

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364 THE DETERMINATION OF HYDROGEN IONS

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366 THE DETERMINATION OF HYDROGEN IONS

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370 THE DETERMINATION OF HYDROGEN IONS

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374 THE DETERMINATION OF HYDROGEN IONS

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376 THE DETERMINATION OF HYDROGEN IONS

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378 THE DETEKMINATION OF HYDROGEN IONS

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380 THE DETERMINATION OF HYDROGEN IONS

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382 THE DETERMINATION OF HYDROGEN IONS

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388 THE DETERMINATION OF HYDROGEN IONS

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390 THE DETERMINATION OF HYDROGEN IONS

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392 THE DETERMINATION OF HYDROGEN IONS

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394 THE DETERMINATION OP HYDROGEN IONS

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Full text of "The determination of hydrogen ions; an elementary treatise on the hydrogen electrode indicator and supplementary methods, with an indexed bibliography on applications"

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